A016208 Expansion of 1/((1-x)*(1-3*x)*(1-4*x)).

1, 8, 45, 220, 1001, 4368, 18565, 77540, 320001, 1309528, 5326685, 21572460, 87087001, 350739488, 1410132405, 5662052980, 22712782001, 91044838248, 364760483725, 1460785327100, 5848371485001, 23409176469808, 93683777468645, 374876324642820, 1499928942876001

Offset

0,2

Comments

Binomial transform of A085277. - Paul Barry, Jun 25 2003

Number of walks of length 2n+5 between two nodes at distance 5 in the cycle graph C_12. - Herbert Kociemba, Jul 05 2004

Links

Muniru A Asiru, Table of n, a(n) for n = 0..1000

Natalia Agudelo Muñetón, Agustín Moreno Cañadas, Pedro Fernando Fernández Espinosa, and Isaías David Marín Gaviria, Brauer Configuration Algebras and Their Applications in Graph Energy Theory, Mathematics (2021) Vol. 9, 3042.

Index entries for linear recurrences with constant coefficients, signature (8,-19,12)

Formula

a(n) = 16*4^n/3 + 1/6 - 9*3^n/2. - Paul Barry, Jun 25 2003

a(0) = 0, a(1) = 8, a(n) = 7*a(n-1) - 12*a(n-2) + 1. - Vincenzo Librandi, Feb 10 2011

a(0) = 1, a(1) = 8, a(2) = 45, a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3). - Harvey P. Dale, Apr 09 2012

Mathematica

Table[(2^(2*n + 3) - 3^(n + 2) + 1)/6, {n, 40}] (* Vladimir Joseph Stephan Orlovsky, Jan 19 2011 *)
CoefficientList[Series[1/((1-x)(1-3x)(1-4x)), {x, 0, 30}], x] (* or *) LinearRecurrence[ {8, -19, 12}, {1, 8, 45}, 30] (* Harvey P. Dale, Apr 09 2012 *)

Prog

(PARI) Vec(1/((1-x)*(1-3*x)*(1-4*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012
(GAP) a:=[1, 8, 45];; for n in [4..30] do a[n]:=8*a[n-1]-19*a[n-2]+12*a[n-3]; od; Print(a); # Muniru A Asiru, Apr 19 2019

Crossrefs

Cf. A000225, A000295, A000392, A002275, A003462, A003463, A003464, A023000, A023001, A002452, A016123, A016125, A016256.

Sequence in context: A273305 A026015 A002696 * A216540 A026852 A317405

Adjacent sequences: A016205 A016206 A016207 * A016209 A016210 A016211

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved