A102841 a(n) = ((9*n^2 + 33*n + 26)*2^n + (-1)^n)/27.

1, 5, 19, 61, 179, 493, 1299, 3309, 8211, 19949, 47635, 112109, 260627, 599533, 1366547, 3089901, 6937107, 15476205, 34331155, 75769325, 166451731, 364127725, 793500179, 1723082221, 3729512979, 8048092653, 17319057939

Offset

0,2

Comments

A floretion-generated sequence relating the number of edges and faces in n-dimensional hypercube.

Equals A001787, (1, 4, 12, 32, 80, ...) convolved with A001045, the Jacobsthal sequence. - Gary W. Adamson, May 23 2009

The sum of the sizes of all inversions in compositions of n. - Arnold Knopfmacher, Jan 22 2020

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

M. Archibald, A. Blecher, A. Knopfmacher, M. E. Mays, Inversions and Parity in Compositions of Integers, J. Int. Seq., Vol. 23 (2020), Article 20.4.1.

Index entries for linear recurrences with constant coefficients, signature (5,-6,-4,8).

Formula

G.f.: 1/((1+x)*(1-2*x)^3).

a(n+1) - 2*a(n) = A045883(n+2).

a(n) + a(n+1) = A001788(n+2).

a(n) = 5*a(n-1) - 6*a(n-2) - 4*a(n-3) + 8*a(n-4). - Wesley Ivan Hurt, Jul 03 2020

Mathematica

Table[(1/27)*((9 n^2 + 33 n + 26) 2^n + (-1)^n), {n, 0, 50}] (* or *) LinearRecurrence[{5, -6, -4, 8}, {1, 5, 19, 61}, 50] (* G. C. Greubel, Sep 27 2017 *)

Prog

(Magma) [((9*n^2 + 33*n + 26)*2^n + (-1)^n)/27 : n in [0..40]]; // Wesley Ivan Hurt, Jul 03 2020

Crossrefs

Cf. A045883, A001788, A001793, A102301.

Cf. A001787, A001045. - Gary W. Adamson, May 23 2009

Sequence in context: A128638 A036630 A338229 * A036637 A036644 A000342

Adjacent sequences: A102838 A102839 A102840 * A102842 A102843 A102844

Keyword

nonn

Author

Creighton Dement, Feb 27 2005

Extensions

Corrected by T. D. Noe, Nov 08 2006

Status

approved