A281084 Expansion of Product_{k>=0} (1 + x^(3*k*(k+1)+1)).

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

Offset: 0

Author

Ilya Gutkovskiy, Jan 14 2017

Keywords

• nonn

Comments

Number of partitions of n into distinct centered hexagonal numbers (A003215).

Examples

			a(98) = 2 because we have [91, 7] and [61, 37].
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Hex Number
• Index entries for sequences related to centered polygonal numbers
• Index entries for related partition-counting sequences

Crossrefs

Cf. A003215, A279279, A280953, A281081, A281082, A281083.

Programs

Mathematica

nmax = 105; CoefficientList[Series[Product[1 + x^(3 k (k + 1) + 1), {k, 0, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=0} (1 + x^(3*k*(k+1)+1)).