Module: FigurateNumbers::MultiDimensionalFigurateNumbers

Extended by:
MultiDimensionalFigurateNumbers
Included in:
FigurateNumbers, MultiDimensionalFigurateNumbers
Defined in:
lib/figurate_numbers/multidimensional_figurate_numbers.rb

Overview

Module containing methods for generating n-dimensional figurate number sequences.

Instance Method Summary collapse

Instance Method Details

#apocalyptic ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 824

def apocalyptic
  Enumerator.new do |y|
    (157..Float::INFINITY).each do |delta|
      y << helper_apocalyptic(delta) unless helper_apocalyptic(delta).nil?
    end
  end
end

#binomial_coefficient_k_dimensional_hypertetrahedron(k) ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 59

def binomial_coefficient_k_dimensional_hypertetrahedron(k)
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << Utils.binomial_coefficient(delta + (k - 1), k)
    end
  end
end

#biquadratic ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 67

def biquadratic
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta**4
    end
  end
end

#carmichael ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 779

def carmichael
  Enumerator.new do |y|
    (561..Float::INFINITY).each do |delta|
      num_seq = helper_carmichael(delta)
      y << num_seq unless num_seq.nil?
    end
  end
end

#centered_biquadratic ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 427

def centered_biquadratic
  Enumerator.new do |y|
    a = 0
    (1..Float::INFINITY).each do |delta|
      a += delta**4 - (delta - 2)**4
      y << a + 1
    end
  end
end

#centered_hyperoctahedral ⇒ Object Also known as: orthoplex 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 517

def centered_hyperoctahedral
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (2 * delta**4 - 4 * delta**3 + 10 * delta**2 - 8 * delta + 3) / 3
    end
  end
end

#centered_polytope ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 461

def centered_polytope
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (5 * delta**4 - 10 * delta**3 + 55 * delta**2 - 50 * delta + 24) / 24
    end
  end
end

#cuban ⇒ Object Also known as: cuban_prime 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 719

def cuban
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta + 1)**3 - delta**3
    end
  end
end

#eight_dimensional_hyperoctahedron ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 181

def eight_dimensional_hyperoctahedron
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta**6 + 28 * delta**4 + 154 * delta**2 + 132) * delta**2 / 315
    end
  end
end

#five_dimensional_centered_hypercube ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 445

def five_dimensional_centered_hypercube
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta**5 + (delta - 1)**5
    end
  end
end

#five_dimensional_centered_hyperoctahedron ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 557

def five_dimensional_centered_hyperoctahedron
  Enumerator.new do |y|
    y << 1
    (1..Float::INFINITY).each do |n|
      y << ext_int_double_summation(5, n)
    end
  end
end

#five_dimensional_centered_hypertetrahedron ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 501

def five_dimensional_centered_hypertetrahedron
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |n|
      y << acc_helper_centered_hypertetrahedron(5, n)
    end
  end
end

#five_dimensional_heptagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 349

def five_dimensional_heptagonal_pyramidal
  Enumerator.new do |y|
    k = 5
    m = 7
    (1..Float::INFINITY).each do |delta|
      y << (Utils.pseudo_pochhammer_function(delta, k) * ((m - 2) * delta - m + k + 2)) / Utils.factorial_iter(k)
    end
  end
end

#five_dimensional_hexagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 339

def five_dimensional_hexagonal_pyramidal
  Enumerator.new do |y|
    k = 5
    m = 6
    (1..Float::INFINITY).each do |delta|
      y << (Utils.pseudo_pochhammer_function(delta, k) * ((m - 2) * delta - m + k + 2)) / Utils.factorial_iter(k)
    end
  end
end

#five_dimensional_hypercube ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 85

def five_dimensional_hypercube
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta**5
    end
  end
end

#five_dimensional_hyperoctahedron ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 157

def five_dimensional_hyperoctahedron
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (2 * delta**4 + 10 * delta**2 + 3) / 15
    end
  end
end

#five_dimensional_hypertetrahedron ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 43

def five_dimensional_hypertetrahedron
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << Utils.rising_factorial(delta, 5) / Utils.factorial_iter(5)
    end
  end
end

#five_dimensional_mgonal_pyramidal(m) ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 311

def five_dimensional_mgonal_pyramidal(m)
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta * (delta + 1) * (delta + 2) * (delta + 3) *  ((m - 2) * delta - m + 7)) / 120
    end
  end
end

#five_dimensional_octagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 359

def five_dimensional_octagonal_pyramidal
  Enumerator.new do |y|
    k = 5
    m = 8
    (1..Float::INFINITY).each do |delta|
      y << (Utils.pseudo_pochhammer_function(delta, k) * ((m - 2) * delta - m + k + 2)) / Utils.factorial_iter(k)
    end
  end
end

#five_dimensional_pentagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 329

def five_dimensional_pentagonal_pyramidal
  Enumerator.new do |y|
    k = 5
    m = 5
    (1..Float::INFINITY).each do |delta|
      y << (Utils.pseudo_pochhammer_function(delta, k) * ((m - 2) * delta - m + k + 2)) / Utils.factorial_iter(k)
    end
  end
end

#five_dimensional_square_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 319

def five_dimensional_square_pyramidal
  Enumerator.new do |y|
    k = 5
    m = 4
    (1..Float::INFINITY).each do |delta|
      y << (Utils.pseudo_pochhammer_function(delta, k) * ((m - 2) * delta - m + k + 2)) / Utils.factorial_iter(k)
    end
  end
end

#four_dimensional_decagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 277

def four_dimensional_decagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta * (delta + 1) * (delta + 2) *  ((10 - 2) * delta - 10 + 6)) / 24
    end
  end
end

#four_dimensional_dodecagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 293

def four_dimensional_dodecagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta * (delta + 1) * (delta + 2) *  ((12 - 2) * delta - 12 + 6)) / 24
    end
  end
end

#four_dimensional_hendecagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 285

def four_dimensional_hendecagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta * (delta + 1) * (delta + 2) *  ((11 - 2) * delta - 11 + 6)) / 24
    end
  end
end

#four_dimensional_heptagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 253

def four_dimensional_heptagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta * (delta + 1) * (delta + 2) *  ((7 - 2) * delta - 7 + 6)) / 24
    end
  end
end

#four_dimensional_hexagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 245

def four_dimensional_hexagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta * (delta + 1) * (delta + 2) *  ((6 - 2) * delta - 6 + 6)) / 24
    end
  end
end

#four_dimensional_hyperoctahedron ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 149

def four_dimensional_hyperoctahedron
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta**2 * (delta**2 + 2) / 3
    end
  end
end

#four_dimensional_mgonal_pyramidal(m) ⇒ Object Also known as: mgonal_pyramidal_numbers_of_the_second_order 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 219

def four_dimensional_mgonal_pyramidal(m)
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta * (delta + 1) * (delta + 2) *  ((m - 2) * delta - m + 6)) / 24
    end
  end
end

#four_dimensional_nonagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 269

def four_dimensional_nonagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta * (delta + 1) * (delta + 2) *  ((9 - 2) * delta - 9 + 6)) / 24
    end
  end
end

#four_dimensional_octagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 261

def four_dimensional_octagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta * (delta + 1) * (delta + 2) *  ((8 - 2) * delta - 8 + 6)) / 24
    end
  end
end

#four_dimensional_pentagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 237

def four_dimensional_pentagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta * (delta + 1) * (delta + 2) *  ((5 - 2) * delta - 5 + 6)) / 24
    end
  end
end

#four_dimensional_square_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 229

def four_dimensional_square_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta * (delta + 1) * (delta + 2) *  ((4 - 2) * delta - 4 + 6)) / 24
    end
  end
end

#generalized_biquadratic(left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 591

def generalized_biquadratic(left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << delta**4
    end
  end
end

#generalized_hyperdodecahedral(left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 627

def generalized_hyperdodecahedral(left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << (delta  * (261 * delta**3 - 504 * delta**2 + 283 * delta - 38)) / 2
    end
  end
end

#generalized_hypericosahedral(left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 635

def generalized_hypericosahedral(left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << (delta  * (145 * delta**3 - 280 * delta**2 + 179 * delta - 38)) / 6
    end
  end
end

#generalized_hyperoctahedral(left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 607

def generalized_hyperoctahedral(left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << (delta**2 * (delta**2 + 2)) / 3
    end
  end
end

#generalized_k_dimensional_centered_hypercube(k, left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 659

def generalized_k_dimensional_centered_hypercube(k, left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << delta**k + (delta - 1)**k
    end
  end
end

#generalized_k_dimensional_centered_hyperoctahedron(k, left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 700

def generalized_k_dimensional_centered_hyperoctahedron(k, left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |n|
      y << 1 if n == 1
      y << gen_ext_int_double_summation(k, n) if n != 0
    end
  end
end

#generalized_k_dimensional_centered_hypertetrahedron(k, left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 677

def generalized_k_dimensional_centered_hypertetrahedron(k, left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |n|
      y << gen_acc_helper_centered_hypertetrahedron(k, n)
    end
  end
end

#generalized_k_dimensional_hypercube(k = 5, left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 599

def generalized_k_dimensional_hypercube(k = 5, left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << delta**k
    end
  end
end

#generalized_k_dimensional_hyperoctahedron(k = 5, left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 615

def generalized_k_dimensional_hyperoctahedron(k = 5, left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      a = 0
      (0..(k - 1)).each do |i|
        a += Utils.binomial_coefficient(k - 1, i) * (Utils.rising_factorial(delta - i, k) / Utils.factorial_iter(k))
      end
      y << a
    end
  end
end

#generalized_k_dimensional_hypertetrahedron(k, left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 583

def generalized_k_dimensional_hypertetrahedron(k, left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << Utils.rising_factorial(delta, k) / Utils.factorial_iter(k)
    end
  end
end

#generalized_k_dimensional_mgonal_pyramidal(k, m, left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 651

def generalized_k_dimensional_mgonal_pyramidal(k, m, left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |n|
      y << (Utils.pseudo_pochhammer_function(n, k) * ((m - 2) * n - m + k + 2)) / Utils.factorial_iter(k)
    end
  end
end

#generalized_nexus(k, left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 709

def generalized_nexus(k, left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << (delta + 1)**(k + 1) - delta**(k + 1)
    end
  end
end

#generalized_pentatope(left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 575

def generalized_pentatope(left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (delta + 2) * (delta + 3) / 24
    end
  end
end

#generalized_polyoctahedral(left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 643

def generalized_polyoctahedral(left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << delta**2 * (3 * delta**2 - 4 * delta + 2)
    end
  end
end

#hyperdodecahedral ⇒ Object Also known as: hecatonicosachoron, dodecaplex, polydodecahedron 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 125

def hyperdodecahedral
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta  * (261 * delta**3 - 504 * delta**2 + 283 * delta - 38)) / 2
    end
  end
end

#hypericosahedral ⇒ Object Also known as: tetraplex, polytetrahedron, hexacosichoron 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 113

def hypericosahedral
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta  * (145 * delta**3 - 280 * delta**2 + 179 * delta - 38)) / 6
    end
  end
end

#hyperoctahedral ⇒ Object Also known as: hexadecachoron, four_cross_polytope, four_orthoplex 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 101

def hyperoctahedral
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta**2 * (delta**2 + 2)) / 3
    end
  end
end

#k_dimensional_centered_hypercube(k) ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 437

def k_dimensional_centered_hypercube(k)
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta**k + (delta - 1)**k
    end
  end
end

#k_dimensional_centered_hyperoctahedron(k) ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 548

def k_dimensional_centered_hyperoctahedron(k)
  Enumerator.new do |y|
    y << 1
    (1..Float::INFINITY).each do |n|
      y << ext_int_double_summation(k, n)
    end
  end
end

#k_dimensional_centered_hypertetrahedron(k) ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 493

def k_dimensional_centered_hypertetrahedron(k)
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |n|
      y << acc_helper_centered_hypertetrahedron(k, n)
    end
  end
end

#k_dimensional_hypercube(k) ⇒ Object Also known as: k_hypercube 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 75

def k_dimensional_hypercube(k)
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta**k
    end
  end
end

#k_dimensional_hyperoctahedron(k) ⇒ Object Also known as: k_cross_polytope 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 205

def k_dimensional_hyperoctahedron(k)
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      a = 0
      (0..(k - 1)).each do |i|
        a += Utils.binomial_coefficient(k - 1, i) * (Utils.rising_factorial(delta - i, k) / Utils.factorial_iter(k))
      end
      y << a
    end
  end
end

#k_dimensional_hypertetrahedron(k) ⇒ Object Also known as: k_hypertetrahedron, regular_k_polytopic, figurate_numbers_of_order_k 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 27

def k_dimensional_hypertetrahedron(k)
  Enumerator.new do |y|
    delta = 1
    bin_coeff = 1
    loop do
      y << bin_coeff
      bin_coeff = bin_coeff * (delta + k) / delta
      delta += 1
    end
  end
end

#k_dimensional_mgonal_pyramidal(k, m) ⇒ Object Also known as: mgonal_pyramidal_numbers_of_the_k_2_th_order 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 301

def k_dimensional_mgonal_pyramidal(k, m)
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |n|
      y << (Utils.pseudo_pochhammer_function(n, k) * ((m - 2) * n - m + k + 2)) / Utils.factorial_iter(k)
    end
  end
end

#nexus(k) ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 527

def nexus(k)
  Enumerator.new do |y|
    (0..Float::INFINITY).each do |delta|
      y << (delta + 1)**(k + 1) - delta**(k + 1)
    end
  end
end

#nine_dimensional_hyperoctahedron ⇒ Object

rubocop:disable Metrics/AbcSize



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 189

def nine_dimensional_hyperoctahedron # rubocop:disable Metrics/AbcSize
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (2 * delta**8 + 84 * delta**6 + 798 * delta**4 + 1636 * delta**2 + 315) * delta / 2835
    end
  end
end

#pell ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 750

def pell
  pell_numbers = [0, 1]
  Enumerator.new do |y|
    y << 0
    y << 1
    (2..Float::INFINITY).each do |delta|
      y << pell_numbers[delta] = 2 * pell_numbers[delta - 1] + pell_numbers[delta - 2]
    end
  end
end

#pentatope ⇒ Object Also known as: hypertetrahedral, triangulotriangular 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 8

def pentatope
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta * (delta + 1) * (delta + 2) * (delta + 3)) / 24
    end
  end
end

#polyoctahedral ⇒ Object Also known as: icositetrachoron, octaplex, hyperdiamond 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 137

def polyoctahedral
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta**2 * (3 * delta**2 - 4 * delta + 2)
    end
  end
end

#quartan ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 742

def quartan
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << helper_quartan(delta)[delta - 1]
    end
  end
end

#reference_of_book_k_dimensional_hypertetrahedron(k) ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 19

def reference_of_book_k_dimensional_hypertetrahedron(k)
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << Utils.rising_factorial(delta, k) / Utils.factorial_iter(k)
    end
  end
end

#seven_dimensional_hyperoctahedron ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 173

def seven_dimensional_hyperoctahedron
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (4 * delta**6 + 70 * delta**4 + 196 * delta**2 + 45) * delta / 315
    end
  end
end

#six_dimensional_centered_hypercube ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 453

def six_dimensional_centered_hypercube
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta**6 + (delta - 1)**6
    end
  end
end

#six_dimensional_centered_hyperoctahedron ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 566

def six_dimensional_centered_hyperoctahedron
  Enumerator.new do |y|
    y << 1
    (1..Float::INFINITY).each do |n|
      y << ext_int_double_summation(6, n)
    end
  end
end

#six_dimensional_centered_hypertetrahedron ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 509

def six_dimensional_centered_hypertetrahedron
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |n|
      y << acc_helper_centered_hypertetrahedron(6, n)
    end
  end
end

#six_dimensional_heptagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 407

def six_dimensional_heptagonal_pyramidal
  Enumerator.new do |y|
    k = 6
    m = 7
    (1..Float::INFINITY).each do |delta|
      y << (Utils.pseudo_pochhammer_function(delta, k) * ((m - 2) * delta - m + k + 2)) / Utils.factorial_iter(k)
    end
  end
end

#six_dimensional_hexagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 397

def six_dimensional_hexagonal_pyramidal
  Enumerator.new do |y|
    k = 6
    m = 6
    (1..Float::INFINITY).each do |delta|
      y << (Utils.pseudo_pochhammer_function(delta, k) * ((m - 2) * delta - m + k + 2)) / Utils.factorial_iter(k)
    end
  end
end

#six_dimensional_hypercube ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 93

def six_dimensional_hypercube
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta**6
    end
  end
end

#six_dimensional_hyperoctahedron ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 165

def six_dimensional_hyperoctahedron
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta**2 * (2 * delta**4 + 20 * delta**2 + 23) / 45
    end
  end
end

#six_dimensional_hypertetrahedron ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 51

def six_dimensional_hypertetrahedron
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << Utils.rising_factorial(delta, 6) / Utils.factorial_iter(6)
    end
  end
end

#six_dimensional_mgonal_pyramidal(m) ⇒ Object

rubocop:disable Metrics/AbcSize



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 369

def six_dimensional_mgonal_pyramidal(m) # rubocop:disable Metrics/AbcSize
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta * (delta + 1) * (delta + 2) * (delta + 3) * (delta + 4) * ((m - 2) * delta - m + 8)) / 720
    end
  end
end

#six_dimensional_octagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 417

def six_dimensional_octagonal_pyramidal
  Enumerator.new do |y|
    k = 6
    m = 8
    (1..Float::INFINITY).each do |delta|
      y << (Utils.pseudo_pochhammer_function(delta, k) * ((m - 2) * delta - m + k + 2)) / Utils.factorial_iter(k)
    end
  end
end

#six_dimensional_pentagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 387

def six_dimensional_pentagonal_pyramidal
  Enumerator.new do |y|
    k = 6
    m = 5
    (1..Float::INFINITY).each do |delta|
      y << (Utils.pseudo_pochhammer_function(delta, k) * ((m - 2) * delta - m + k + 2)) / Utils.factorial_iter(k)
    end
  end
end

#six_dimensional_square_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 377

def six_dimensional_square_pyramidal
  Enumerator.new do |y|
    k = 6
    m = 4
    (1..Float::INFINITY).each do |delta|
      y << (Utils.pseudo_pochhammer_function(delta, k) * ((m - 2) * delta - m + k + 2)) / Utils.factorial_iter(k)
    end
  end
end

#stern_prime(infty = false) ⇒ Object

rubocop:disable Style/OptionalBooleanParameter



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 803

def stern_prime(infty = false) # rubocop:disable Style/OptionalBooleanParameter
  Enumerator.new do |y|
    max_term = infty == false ? 238 : float::INFINITY
    (1..max_term).each do |delta|
      num_seq = helper_stern_prime(delta)
      y << num_seq unless num_seq.nil?
    end
  end
end

#ten_dimensional_hyperoctahedron ⇒ Object

rubocop:disable Metrics/AbcSize



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# File 'lib/figurate_numbers/multidimensional_figurate_numbers.rb', line 197

def ten_dimensional_hyperoctahedron # rubocop:disable Metrics/AbcSize
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (2 * delta**8 + 120 * delta**6 + 1806 * delta**4 + 7180 * delta**2 + 5067) * delta**2 / 14_175
    end
  end
end