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

Author

Ilya Gutkovskiy, Jan 15 2018

Keywords

• nonn

Comments

Number of partitions of n into distinct square pyramidal numbers.

Examples

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

Links

• Eric Weisstein's World of Mathematics, Square Pyramidal Number
• Index entries for related partition-counting sequences

Crossrefs

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

Programs

Mathematica

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

Formula

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