A234274 Expansion of g.f. (1+x)*(1+x+x^2+x^3+x^4)/(1-6*x-6*x^2-6*x^3+x^4).

1, 8, 56, 392, 2737, 19103, 133336, 930664, 6495881, 45340183, 316467032, 2208887912, 15417674881, 107612838767, 751119942328, 5242693847944, 36593142099353, 255414122498983, 1782748630735352, 12443292678154184, 86852139446231761, 606213670408228799, 4231271866564953112

Offset

0,2

Links

Table of n, a(n) for n=0..22.

J. Choi, N. Pippenger, Counting the Angels and Devils in Escher's Circle Limit IV, arXiv preprint arXiv:1310.1357 [math.CO], 2013.

Index entries for linear recurrences with constant coefficients, signature (6, 6, 6, -1).

Formula

G.f.: (1+x)*(1+x+x^2+x^3+x^4)/(1-6*x-6*x^2-6*x^3+x^4).

a(n) = 6*a(n-1) + 6*a(n-2) + 6*a(n-3) - a(n-4). - Wesley Ivan Hurt, Jul 07 2025

Mathematica

Join[{1, 8}, LinearRecurrence[{6, 6, 6, -1}, {56, 392, 2737, 19103}, 21]] (* Jean-François Alcover, Feb 12 2019 *)

Crossrefs

Sequence in context: A010575 A162949 A063812 * A163347 A163924 A164373

Adjacent sequences: A234271 A234272 A234273 * A234275 A234276 A234277

Keyword

nonn

Author

N. J. A. Sloane, Dec 24 2013

Status

approved