A374900 Expansion of Sum_{k in Z} x^k / (1 - x^(7*k+1)).

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

Offset

0,2

Links

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

Formula

G.f.: Product_{k>0} (1-x^(7*k))^2 * (1-x^(7*k-2)) * (1-x^(7*k-5)) / ((1-x^(7*k-1)) * (1-x^(7*k-6)))^2.

Prog

(PARI) my(N=110, x='x+O('x^N)); Vec(sum(k=-N, N, x^k/(1-x^(7*k+1))))
(PARI) my(N=110, x='x+O('x^N)); Vec(prod(k=1, N, (1-x^(7*k))^2*(1-x^(7*k-2))*(1-x^(7*k-5))/((1-x^(7*k-1))*(1-x^(7*k-6)))^2))

Crossrefs

Cf. A008441, A033687, A097195, A340456.

Sequence in context: A297031 A229895 A063982 * A318882 A327160 A355832

Adjacent sequences: A374897 A374898 A374899 * A374901 A374902 A374903

Keyword

nonn

Author

Seiichi Manyama, Jul 31 2024

Status

approved