A279484 Expansion of Product_{k>=1} (1-x^(k^3)).

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

Offset

0

Comments

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

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..100000

Mathematica

nn = 10; CoefficientList[Series[Product[(1-x^(k^3)), {k, nn}], {x, 0, nn^3}], x]
nmax = 1000; nn = Floor[nmax^(1/3)]+1; poly = ConstantArray[0, nn^3 + 1]; poly[[1]] = 1; poly[[2]] = -1; poly[[3]] = 0; Do[Do[poly[[j + 1]] -= poly[[j - k^3 + 1]], {j, nn^3, k^3, -1}]; , {k, 2, nn}]; Take[poly, nmax+1]

Crossrefs

Cf. A010815, A276516.

Cf. A000009, A033461, A279329.

Cf. A279486.

Sequence in context: A204220 A281814 A353566 * A279329 A374117 A359430

Adjacent sequences: A279481 A279482 A279483 * A279485 A279486 A279487

Keyword

sign

Author

Vaclav Kotesovec, Dec 13 2016

Status

approved