A284585 Expansion of Product_{k>=0} (1 - x^(6*k+1)) in powers of x.

1, -1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 2, -1, 0, 0, 0, -1, 2, -1, 0, 0, 0, -1, 3, -2, 0, 0, 0, -1, 3, -3, 1, 0, 0, -1, 4, -4, 1, 0, 0, -1, 4, -5, 2, 0, 0, -1, 5, -7, 3, 0, 0, -1, 5, -8, 5, -1, 0, -1, 6, -10, 6, -1, 0, -1, 6, -12, 9, -2, 0, -1

Offset: 0

Author

Seiichi Manyama, Mar 29 2017

Keywords

• sign

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. Product_{k>=0} (1 - x^(6*k+m)): this sequence (m=1), A284586 (m=5).

Cf. A280456.

Programs

Maple

N:= 100: # to get a(0)..a(N)
V:= Vector(N+1):
V[1]:= 1:
for k from 0 to floor((N-1)/6) do
V[6*k+2..N+1]:= V[6*k+2..N+1]+V[1..N-6*k]
od:
seq((-1)^n*V[n+1],n=0..N); # Robert Israel, Apr 09 2017

Mathematica

CoefficientList[Series[Product[1 - x^(6*k+1), {k, 0, 79}], {x, 0, 79}], x] (* Indranil Ghosh, Mar 29 2017 *)

Formula

a(n) = -(1/n)*Sum_{k=1..n} A284098(k)*a(n-k), a(0) = 1.

a(n) = (-1)^n * A280456(n). - Robert Israel, Apr 09 2017