A284315 Expansion of Product_{k>=0} (1 - x^(3*k+2)) in powers of x.

1, 0, -1, 0, 0, -1, 0, 1, -1, 0, 1, -1, 0, 2, -1, -1, 2, -1, -1, 3, -1, -2, 3, -1, -3, 4, 0, -4, 4, 0, -5, 5, 1, -7, 5, 2, -8, 6, 4, -10, 5, 5, -12, 6, 8, -14, 5, 10, -16, 5, 14, -19, 3, 17, -21, 2, 22, -23, -1, 26, -26, -3, 33, -28, -8, 38, -30, -12, 46, -32, -19

Offset: 0

Author

Seiichi Manyama, Mar 25 2017

Keywords

• sign
• look

Links

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

Crossrefs

Cf. Product_{k>=0} (1 - x^(m*k+m-1)): A081362 (m=2), this sequence (m=3), A284316 (m=4), A284317 (m=5).

Cf. A078182, A262928.

Programs

Mathematica

CoefficientList[Series[Product[1 - x^(3k + 2), {k, 0, 100}], {x, 0, 100}], x] (* Indranil Ghosh, Mar 25 2017 *)

PARI

Vec(prod(k=0, 100, 1 - x^(3*k+2)) + O(x^101)) \\ Indranil Ghosh, Mar 25 2017

Formula

a(n) = -(1/n) * Sum_{k=1..n} A078182(k) * a(n-k), a(0) = 1.