A298246 Expansion of Product_{k>=1} (1 + x^(k*(k+1)*(2*k+1)/6)).

1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1

Offset

0,92

Comments

Number of partitions of n into distinct square pyramidal numbers.

Links

Table of n, a(n) for n=0..104.

Eric Weisstein's World of Mathematics, Square Pyramidal Number

Index entries for related partition-counting sequences

Formula

G.f.: Product_{k>=1} (1 + x^A000330(k)).

Example

a(91) = 2 because we have [91] and [55, 30, 5, 1].

Mathematica

nmax = 104; CoefficientList[Series[Product[1 + x^(k (k + 1) (2 k + 1)/6), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000330, A033461, A279220, A279278, A289895.

Sequence in context: A015624 A015114 A016219 * A279024 A213731 A299197

Adjacent sequences: A298243 A298244 A298245 * A298247 A298248 A298249

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 15 2018

Status

approved