A363801 Expansion of Product_{k>0} (1 - x^(7*k-4)) * (1 - x^(7*k-3)) * (1 - x^(7*k)).

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

Offset

0

Links

Table of n, a(n) for n=0..100.

Formula

G.f.: Sum_{k in Z} (-1)^k * x^(k * (7*k + 1) / 2).

a(0) = 1; a(n) = -(1/n) * Sum_{k=1..n} A363804(k) * a(n-k).

Prog

(PARI) my(N=100, x='x+O('x^N)); Vec(prod(k=1, N, 1-[1, 0, 0, 1, 1, 0, 0][k%7+1]*x^k))

Crossrefs

Convolution inverse of A346798.

Cf. A232714, A363800.

Cf. A022264, A022265, A363804.

Sequence in context: A325899 A126999 A306862 * A347283 A214293 A323096

Adjacent sequences: A363798 A363799 A363800 * A363802 A363803 A363804

Keyword

sign

Author

Seiichi Manyama, Jun 23 2023

Status

approved