A306157 Inverse Weigh transform of 3^n.

3, 6, 8, 24, 48, 124, 312, 834, 2184, 5928, 16104, 44344, 122640, 341796, 956576, 2690844, 7596480, 21524412, 61171656, 174342192, 498111952, 1426419852, 4093181688, 11767919284, 33891544368, 97764131640, 282429535752, 817028472936, 2366564736720, 6863038212784

Offset

1,1

Links

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

N. J. A. Sloane, Transforms

Formula

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

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

Example

(1+x)^3*(1+x^2)^6*(1+x^3)^8*(1+x^4)^24* ... = 1 + 3*x + 9*x^2 + 27*x^3 + 81*x^4 + ... .

Crossrefs

Inverse Weigh transform of b^n: A306156 (b=2), this sequence (b=3), A306158 (b=4), A306159 (b=5).

Cf. A000244, A038068.

Sequence in context: A278486 A038064 A093899 * A262613 A137129 A098106

Adjacent sequences: A306154 A306155 A306156 * A306158 A306159 A306160

Keyword

nonn

Author

Seiichi Manyama, Jun 23 2018

Status

approved