A383034 Inverse Weigh transform of 2^(n-1).

1, 2, 2, 5, 6, 11, 18, 35, 56, 105, 186, 346, 630, 1179, 2182, 4115, 7710, 14588, 27594, 52482, 99858, 190743, 364722, 699216, 1342176, 2581425, 4971008, 9587574, 18512790, 35792449, 69273666, 134219795, 260300986, 505294125, 981706806, 1908881548, 3714566310

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..3000

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

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

Formula

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

a(n) = A306156(n) - A209229(n).

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

Crossrefs

Column k=2 of A383033.

Cf. A000079, A209229, A306156.

Sequence in context: A238517 A335240 A356367 * A365825 A099926 A355021

Adjacent sequences: A383031 A383032 A383033 * A383035 A383036 A383037

Keyword

nonn

Author

Seiichi Manyama, Apr 13 2025

Status

approved