A281082 Expansion of Product_{k>=0} (1 + x^(2*k*(k+1)+1)).

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

Offset: 0

Author

Ilya Gutkovskiy, Jan 14 2017

Keywords

• nonn

Comments

Number of partitions of n into distinct centered square numbers (A001844).

Examples

			a(66) = 2 because we have [61, 5] and [41, 25].
		

Links

• Eric Weisstein's World of Mathematics, Centered Square Number
• Index entries for sequences related to centered polygonal numbers
• Index entries for related partition-counting sequences

Crossrefs

Cf. A001844, A033461, A280951, A281081, A281083, A281084.

Programs

Mathematica

nmax = 105; CoefficientList[Series[Product[1 + x^(2 k (k + 1) + 1), {k, 0, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=0} (1 + x^(2*k*(k+1)+1)).