# Figurate Numbers v1.6.0 - Sonic Pi Web
# Source: https://github.com/edelveart/figurate_numbers
# Author: Edgar Delgado Vega
# Bundle: space_figurate_numbers

module FigurateNumbers;module SpaceFigurateNumbers
extend self;def r_pyramidal(r=3)Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(3*delta**2+delta**3*(r-2)-delta*(r-5))/6;end;end;end;def square_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(delta*(delta+1)*(2*delta+1))/6;end;end;end;alias pyramidal square_pyramidal;def pentagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta**2*(delta+1)/2;end;end;end;def hexagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(4*delta-1)/6;end;end;end;def heptagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(5*delta-2)/6;end;end;end;def octagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(6*delta-3)/6;end;end;end;def nonagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(7*delta-4)/6;end;end;end;def decagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(8*delta-5)/6;end;end;end;def hendecagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(9*delta-6)/6;end;end;end;def dodecagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(10*delta-7)/6;end;end;end;def tridecagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(11*delta-8)/6;end;end;end;def tetradecagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(12*delta-9)/6;end;end;end;def pentadecagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(13*delta-10)/6;end;end;end;def hexadecagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(14*delta-11)/6;end;end;end;def heptadecagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(15*delta-12)/6;end;end;end;def octadecagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(16*delta-13)/6;end;end;end;def nonadecagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(17*delta-14)/6;end;end;end;def icosagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(18*delta-15)/6;end;end;end;def icosihenagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(19*delta-16)/6;end;end;end;def icosidigonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(20*delta-17)/6;end;end;end;def icositrigonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(21*delta-18)/6;end;end;end;def icositetragonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(22*delta-19)/6;end;end;end;def icosipentagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(23*delta-20)/6;end;end;end;def icosihexagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(24*delta-21)/6;end;end;end;def icosiheptagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(25*delta-22)/6;end;end;end;def icosioctagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(26*delta-23)/6;end;end;end;def icosinonagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(27*delta-24)/6;end;end;end;def triacontagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta+1)*(28*delta-25)/6;end;end;end;def triangular_tetrahedral;Enumerator.new do |y|finite_set=[1,10,120,1540,7140];(0..Float::INFINITY).each do |delta|y<<finite_set[delta%5];end;end;end;def triangular_square_pyramidal;Enumerator.new do |y|finite_set=[1,55,91,208_335];(0..Float::INFINITY).each do |delta|y<<finite_set[delta%4];end;end;end;def square_tetrahedral;Enumerator.new do |y|finite_set=[1,4,19_600];(0..Float::INFINITY).each do |delta|y<<finite_set[delta%3];end;end;end;def square_square_pyramidal;Enumerator.new do |y|finite_set=[1,4900];(0..Float::INFINITY).each do |delta|y<<finite_set[delta%2];end;end;end;def tetrahedral_square_pyramidal_number;Enumerator.new do |y|(1..Float::INFINITY).each do y<<1;end;end;end;def cubic;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta**3;end;end;end;alias perfect_cube cubic;def tetrahedral;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(delta*(delta+1)*(delta+2))/6;end;end;end;alias triangular_pyramidal tetrahedral;def octahedral;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(delta*(2*delta**2+1))/3;end;end;end;def dodecahedral;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(delta*(3*delta-1)*(3*delta-2))/2;end;end;end;def icosahedral;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(delta*(5*delta**2-5*delta+2))/2;end;end;end;def truncated_tetrahedral;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(23*delta**2-27*delta+10)*delta/6;end;end;end;def truncated_cubic;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(3*delta-2)**3-((8*(delta-1)*delta*(delta+1))/6);end;end;end;def truncated_octahedral;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(16*delta**3-33*delta**2+24*delta-6);end;end;end;def stella_octangula;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(2*delta**2-1);end;end;end;def centered_cube;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(2*delta-1)*(delta**2-delta+1);end;end;end;def rhombic_dodecahedral;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(2*delta-1)*(2*delta**2-2*delta+1);end;end;end;def hauy_rhombic_dodecahedral;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(2*delta-1)*(8*delta**2-14*delta+7);end;end;end;def centered_tetrahedron;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(2*delta-1)*((delta**2-delta+3))/3;end;end;end;alias centered_tetrahedral centered_tetrahedron;def centered_square_pyramid;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(2*delta-1)*((delta**2-delta+2))/2;end;end;end;alias centered_pyramid centered_square_pyramid;def centered_mgonal_pyramid(m)Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(m-1)*((delta-1)*delta*(2*delta-1))/6+(2*delta-1);end;end;end;def centered_pentagonal_pyramid;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(2*delta-1)*(2*delta**2-2*delta+3)/3;end;end;end;def centered_hexagonal_pyramid;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(2*delta-1)*(5*delta**2-5*delta+6)/6;end;end;end;def centered_heptagonal_pyramid;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(2*delta-1)*(delta**2-delta+1);end;end;end;def centered_octagonal_pyramid;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(2*delta-1)*(7*delta**2-7*delta+6)/6;end;end;end;def centered_octahedron;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(2*delta-1)*(2*delta**2-2*delta+3)/3;end;end;end;def centered_icosahedron;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(2*delta-1)*(5*delta**2-5*delta+3)/3;end;end;end;alias centered_cuboctahedron centered_icosahedron;def centered_dodecahedron;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(2*delta-1)*(3*delta**2-3*delta+1);end;end;end;def centered_truncated_tetrahedron;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(2*delta-1)*(7*delta**2-7*delta+3)/3;end;end;end;def centered_truncated_cube;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(2*delta-1)*(23*delta**2-23*delta+3)/3;end;end;end;def centered_truncated_octahedron;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(2*delta-1)*(5*delta**2-5*delta+1);end;end;end;def centered_mgonal_pyramidal(m)Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(m*delta**3+delta*(6-m))/6;end;end;end;def centered_triangular_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(delta**2+1)/2;end;end;end;def centered_square_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(2*delta**3+delta)/3;end;end;end;def centered_pentagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(5*delta**3+delta)/6;end;end;end;def centered_hexagonal_pyramidal;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta**3;end;end;end;alias hex_pyramidal centered_hexagonal_pyramidal;def centered_heptagonal_pyramidal;m=7;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(m*delta**3+delta*(6-m))/6;end;end;end;def centered_octagonal_pyramidal;m=8;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(m*delta**3+delta*(6-m))/6;end;end;end;def centered_nonagonal_pyramidal;m=9;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(m*delta**3+delta*(6-m))/6;end;end;end;def centered_decagonal_pyramidal;m=10;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(m*delta**3+delta*(6-m))/6;end;end;end;def centered_hendecagonal_pyramidal;m=11;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(m*delta**3+delta*(6-m))/6;end;end;end;def centered_dodecagonal_pyramidal;m=12;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<(m*delta**3+delta*(6-m))/6;end;end;end;def hexagonal_prism;Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(3*delta**2-3*delta+1);end;end;end;def mgonal_prism(m)Enumerator.new do |y|(1..Float::INFINITY).each do |delta|y<<delta*(m*delta**2-m*delta+2)/2;end;end;end;def generalized_mgonal_pyramidal(m,left_index=0)Enumerator.new do |y|((-1*left_index.abs)..Float::INFINITY).each do |delta|y<<(delta*(delta+1)*((m-2)*delta-m+5))/6;end;end;end;def generalized_pentagonal_pyramidal(left_index=0)m=5;Enumerator.new do |y|((-1*left_index.abs)..Float::INFINITY).each do |delta|y<<(delta*(delta+1)*((m-2)*delta-m+5))/6;end;end;end;def generalized_hexagonal_pyramidal(left_index=0)m=6;Enumerator.new do |y|((-1*left_index.abs)..Float::INFINITY).each do |delta|y<<(delta*(delta+1)*((m-2)*delta-m+5))/6;end;end;end;def generalized_cubic(left_index=0)Enumerator.new do |y|((-1*left_index.abs)..Float::INFINITY).each do |delta|y<<delta**3;end;end;end;def generalized_octahedral(left_index=0)Enumerator.new do |y|((-1*left_index.abs)..Float::INFINITY).each do |delta|y<<(2*delta**2+1)*delta/3;end;end;end;def generalized_icosahedral(left_index=0)Enumerator.new do |y|((-1*left_index.abs)..Float::INFINITY).each do |delta|y<<(5*delta**2-5*delta+2)*delta/2;end;end;end;def generalized_dodecahedral(left_index=0)Enumerator.new do |y|((-1*left_index.abs)..Float::INFINITY).each do |delta|y<<(9*delta**2-9*delta+2)*delta/2;end;end;end;def generalized_centered_cube(left_index=0)Enumerator.new do |y|((-1*left_index.abs)..Float::INFINITY).each do |delta|y<<(2*delta-1)*(delta**2-delta+1);end;end;end;def generalized_centered_tetrahedron(left_index=0)Enumerator.new do |y|((-1*left_index.abs)..Float::INFINITY).each do |delta|y<<(2*delta-1)*(delta**2-delta+3)/3;end;end;end;def generalized_centered_square_pyramid(left_index=0)Enumerator.new do |y|((-1*left_index.abs)..Float::INFINITY).each do |delta|y<<((2*delta-1)*(delta**2-delta+2))/2;end;end;end;def generalized_rhombic_dodecahedral(left_index=0)Enumerator.new do |y|((-1*left_index.abs)..Float::INFINITY).each do |delta|y<<delta**4-(delta-1)**4;end;end;end;def generalized_centered_mgonal_pyramidal(m,left_index=0)Enumerator.new do |y|((-1*left_index.abs)..Float::INFINITY).each do |delta|y<<(m*delta**3+delta*(6-m))/6;end;end;end;def generalized_mgonal_prism(m,left_index=0)Enumerator.new do |y|((-1*left_index.abs)..Float::INFINITY).each do |delta|y<<delta*(m*delta**2-m*delta+2)/2;end;end;end;def generalized_hexagonal_prism(left_index=0)Enumerator.new do |y|((-1*left_index.abs)..Float::INFINITY).each do |delta|y<<delta*(3*delta**2-3*delta+1);end;end;end;end;end;module FigurateNumbers;extend SpaceFigurateNumbers;end;SpaceFigurateNumbers=FigurateNumbers::SpaceFigurateNumbers