A284312 Expansion of Product_{k>=0} (1 - x^(3*k+1)) in powers of x.

1, -1, 0, 0, -1, 1, 0, -1, 1, 0, -1, 2, -1, -1, 2, -1, -1, 3, -2, -1, 3, -3, 0, 4, -4, 0, 4, -5, 1, 5, -7, 2, 5, -8, 4, 5, -10, 5, 5, -12, 8, 5, -14, 10, 4, -16, 14, 3, -19, 17, 1, -20, 22, -1, -23, 26, -4, -25, 33, -8, -27, 38, -13, -28, 46, -19, -30, 53, -26, -29

Offset: 0

Author

Seiichi Manyama, Mar 24 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. Product_{k>=0} (1 - x^(m*k+1)): A081362 (m=2), this sequence (m=3), A284313 (m=4), A284314 (m=5).

Cf. A078181, A261612.

Programs

Mathematica

CoefficientList[Series[Product[1 - x^(3k + 1), {k, 0, 100}], {x, 0, 100}], x] (* Indranil Ghosh, Mar 25 2017 *)

PARI

Vec(prod(k=0, 100, 1 - x^(3*k + 1)) + O(x^101)) \\ Indranil Ghosh, Mar 25 2017

Formula

a(n) = -(1/n)*Sum_{k=1..n} A078181(k)*a(n-k), a(0) = 1.