A279485 Expansion of Product_{k>=1} (1-x^(k^4)).

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

Offset

0

Comments

The difference between the number of partitions of n into an even number of distinct fourth powers and the number of partitions of n into an odd number of distinct fourth powers. - Ilya Gutkovskiy, Jan 27 2018

Links

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

Mathematica

nn = 6; CoefficientList[Series[Product[(1-x^(k^4)), {k, nn}], {x, 0, nn^4}], x]
nmax = 1000; nn = Floor[nmax^(1/4)]+1; poly = ConstantArray[0, nn^4 + 1]; poly[[1]] = 1; poly[[2]] = -1; poly[[3]] = 0; Do[Do[poly[[j + 1]] -= poly[[j - k^4 + 1]], {j, nn^4, k^4, -1}]; , {k, 2, nn}]; Take[poly, nmax+1]

Crossrefs

Cf. A010815, A276516, A279484.

Cf. A000009, A033461, A279329.

Sequence in context: A016422 A016399 A016383 * A298859 A216280 A370118

Adjacent sequences: A279482 A279483 A279484 * A279486 A279487 A279488

Keyword

sign

Author

Vaclav Kotesovec, Dec 13 2016

Status

approved