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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved