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A276516 Expansion of Product_{k>=1} (1-x^(k^2)). 13
1, -1, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 1, -1, 0, -1, 1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, -1, 1, 1, 0, -1, 0, 0, 0, 0, 0, 0, -2, 1, 1, 1, 0, 0, -1, -1, 1, 1, -1, 0, 0, -1, 1, -1, 2, -1, 0, 1, -2, 0, 1, 0, 1, 0, -1, 0, -2, 2, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,50

COMMENTS

The difference between the number of partitions of n into an even number of distinct squares and the number of partitions of n into an odd number of distinct squares. - Ilya Gutkovskiy, Jan 15 2018

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Martin Klazar, What is an answer? ā€” remarks, results and problems on PIO formulas in combinatorial enumeration, part I, arXiv:1808.08449, 2018.

MATHEMATICA

nn = 15; CoefficientList[Series[Product[(1-x^(k^2)), {k, nn}], {x, 0, nn^2}], x]

nmax = 200; nn = Floor[Sqrt[nmax]]+1; poly = ConstantArray[0, nn^2 + 1]; poly[[1]] = 1; poly[[2]] = -1; poly[[3]] = 0; Do[Do[poly[[j + 1]] -= poly[[j - k^2 + 1]], {j, nn^2, k^2, -1}]; , {k, 2, nn}]; Take[poly, nmax+1]

CROSSREFS

Cf. A001156, A033461, A279360, A279368, A276517.

Sequence in context: A255319 A214088 A005091 * A253638 A086831 A191340

Adjacent sequences:  A276513 A276514 A276515 * A276517 A276518 A276519

KEYWORD

sign,look

AUTHOR

Vaclav Kotesovec, Dec 12 2016

STATUS

approved

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Last modified October 16 00:50 EDT 2018. Contains 316252 sequences. (Running on oeis4.)