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A279757
Expansion of Product_{k>=1} 1/(1 - x^(k*(2*k^2+1)/3)).
2
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 5, 5, 5, 5, 5, 6, 7, 7, 7, 7, 7, 8, 9, 9, 9, 9, 9, 10, 11, 12, 12, 12, 12, 13, 14, 16, 16, 16, 16, 17, 18, 20, 20, 20, 20, 21, 22, 24, 25, 25, 25, 26, 27, 29, 31, 31, 31, 32, 33, 35, 37, 37, 37, 38, 39, 41, 43, 44, 44, 45, 46, 48, 50, 52, 52, 53, 55, 57, 59, 62, 62, 63, 65, 67, 69, 72, 73
OFFSET
0,7
COMMENTS
Number of partitions of n into nonzero octahedral numbers (A005900).
LINKS
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
Eric Weisstein's World of Mathematics, Octahedral Number
OEIS Wiki, Platonic numbers
FORMULA
G.f.: Product_{k>=1} 1/(1 - x^(k*(2*k^2+1)/3)).
EXAMPLE
a(7) = 2 because we have [6, 1] and [1, 1, 1, 1, 1, 1, 1].
MATHEMATICA
nmax=95; CoefficientList[Series[Product[1/(1 - x^(k (2 k^2 + 1)/3)), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 18 2016
STATUS
approved