A279757 Expansion of Product_{k>=1} 1/(1 - x^(k*(2*k^2+1)/3)).

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

Table of n, a(n) for n=0..95.

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

Index entries for related partition-counting sequences

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

Cf. A003108, A005900, A068980, A279758, A279759.

Sequence in context: A137588 A033271 A290792 * A251550 A279221 A357899

Adjacent sequences: A279754 A279755 A279756 * A279758 A279759 A279760

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 18 2016

Status

approved