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
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)
Crossrefs
Programs
-
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
-
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 *) -
PARI
Vec(1/((1-x)*(1-3*x)*(1-4*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012
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
Comments