A383035 Inverse Weigh transform of 3^(n-1).

1, 3, 6, 18, 42, 113, 294, 798, 2128, 5823, 15918, 43998, 122010, 340617, 954394, 2686728, 7588770, 21509824, 61144062, 174289710, 498012094, 1426229109, 4092816966, 11767220068, 33890202192, 97761550215, 282424564744, 817018885362, 2366546223930, 6863002420335

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..2000

Christian G. Bower, PARI programs for transforms, 2007.

N. J. A. Sloane, Maple programs for transforms, 2001-2020.

Formula

a(n) = (1/n) * (3^n - 2^n + Sum_{d<n and d|n} (-1)^(n/d) * d * a(d)).

a(n) = A306157(n) - A306156(n).

Product_{k>=1} (1 + x^k)^a(k) = (1 - 2*x)/(1 - 3*x).

Crossrefs

Column k=3 of A383033.

Cf. A306156, A306157.

Sequence in context: A342583 A007990 A197050 * A354387 A121188 A331678

Adjacent sequences: A383032 A383033 A383034 * A383036 A383037 A383038

Keyword

nonn

Author

Seiichi Manyama, Apr 13 2025

Status

approved