A298600 Expansion of Product_{k>=2} 1/(1 + x^(k^2)).

1, 0, 0, 0, -1, 0, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, 1, -1, 0, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 0, -2, 2, -1, 1, 2, -2, 1, -1, -2, 3, -2, 1, 2, -3, 2, -1, -1, 2, -3, 1, 1, -2, 3, 0, 0, 2, -3, 1, -1, -2, 3, -1, -2, 2

Offset

0,50

Comments

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

Links

Table of n, a(n) for n=0..82.

Index entries for sequences related to sums of squares

Index entries for related partition-counting sequences

Formula

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

Mathematica

nmax = 82; CoefficientList[Series[Product[1/(1 + x^k^2), {k, 2, Floor[Sqrt[nmax]] + 1}], {x, 0, nmax}], x]

Crossrefs

Cf. A001156, A033461, A078134, A276516, A280129, A292520, A298601.

Sequence in context: A323116 A218344 A211272 * A292470 A293681 A293773

Adjacent sequences: A298597 A298598 A298599 * A298601 A298602 A298603

Keyword

sign

Author

Ilya Gutkovskiy, Jan 22 2018

Status

approved