A374058 Expansion of Product_{k>=1} (1 - x^(3*k-2)) * (1 - x^(3*k)).

1, -1, 0, -1, 0, 1, -1, 1, 0, 0, 1, 0, -1, 1, -1, 1, 0, -1, 0, 0, -1, 1, 0, -1, 1, -1, 0, 1, -1, 0, 1, -1, 1, 1, -1, 0, 0, -1, 2, 0, -1, 1, 0, -1, 2, -2, 0, 1, -1, 0, 1, -1, 0, 1, -2, 1, 1, -2, 1, 0, -2, 2, 0, -2, 2, -1, 0, 2, -1, -1, 1, -1, -1, 3, -2, 0, 2, -2, 1, 2, -3, 1, 1, -2, 2, 1

Offset

0,39

Links

Table of n, a(n) for n=0..85.

Ilya Gutkovskiy, Scatterplot of a(n) up to n=10000

Formula

a(0) = 1; a(n) = -(1/n) * Sum_{k=1..n} A082051(k) * a(n-k).

a(0) = 1; a(n) = -Sum_{k=1..n} A035360(k) * a(n-k).

a(n) = Sum_{k=0..n} A010815(k) * A035386(n-k).

Mathematica

nmax = 85; CoefficientList[Series[Product[(1 - x^(3 k - 2)) (1 - x^(3 k)), {k, 1, nmax}], {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = -(1/n) Sum[Plus @@ Select[Divisors[k], Mod[#, 3] != 2 &] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 85}]

Crossrefs

Cf. A010815, A035360, A035386, A081362, A082051, A132463, A137569, A274719, A284312, A374060.

Sequence in context: A332038 A101672 A083731 * A216266 A177416 A087606

Adjacent sequences: A374055 A374056 A374057 * A374060 A374061 A374062

Keyword

sign

Author

Ilya Gutkovskiy, Jun 27 2024

Status

approved