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

0,67

Comments

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

Links

Table of n, a(n) for n=0..105.

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

Formula

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A287086 A180823 A049800 * A204421 A131018 A300067

Adjacent sequences: A281079 A281080 A281081 * A281083 A281084 A281085

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 14 2017

Status

approved