A298601 Expansion of Product_{k>=2} (1 - x^(k^2)).

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

Offset

0,50

Comments

The difference between the number of partitions of n into an even number of distinct squares > 1 and the number of partitions of n into an odd number of distinct squares > 1.

Partial sums of A276516.

Links

Table of n, a(n) for n=0..90.

Index entries for sequences related to sums of squares

Index entries for related partition-counting sequences

Formula

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

Mathematica

nmax = 92; CoefficientList[Series[Product[1 - x^k^2, {k, 2, Floor[Sqrt[nmax]] + 1}], {x, 0, nmax}], x]

Crossrefs

Cf. A001156, A033461, A078134, A276516, A280129, A292520, A298600.

Sequence in context: A360001 A286656 A048484 * A016366 A016427 A326170

Adjacent sequences: A298598 A298599 A298600 * A298602 A298603 A298604

Keyword

sign

Author

Ilya Gutkovskiy, Jan 22 2018

Status

approved