A375148 Expansion of Sum_{k in Z} x^k / (1 - x^(7*k+2)).

1, 1, 2, 1, 1, 1, 2, 1, 2, 0, 2, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 0, 1, 1, 1, 3, 1, 2, 0, 2, 1, 2, 1, 1, 0, 2, 2, 2, 0, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 0, 2, 2, 1, 1, 0, 2, 0, 2, 1, 2, 1, 4, 1, 2, 0, 0, 1, 3, 1, 0, 1, 1, 1, 2, 1, 2, 1, 3, 1, 1, 1, 2, 0, 1, 0, 3, 2, 1, 1, 0, 2, 2, 1, 4, 0, 0

Offset: 0

Author

Seiichi Manyama, Aug 01 2024

Keywords

• nonn

Crossrefs

Cf. A374900, A375106, A375149, A375150.

Cf. A033687, A340453.

Programs

PARI

my(N=110, x='x+O('x^N)); Vec(sum(k=-N, N, x^k/(1-x^(7*k+2))))

PARI

my(N=110, x='x+O('x^N)); Vec(prod(k=1, N, (1-x^(7*k))^3*((1-x^(7*k-3))*(1-x^(7*k-4)))^2/(1-x^k)))

Formula

G.f.: Product_{k>0} (1-x^(7*k))^3 * ((1-x^(7*k-3)) * (1-x^(7*k-4)))^2 / (1-x^k).

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