OFFSET
0,2
COMMENTS
Let G_n be the graph with vertices {(a,b) : 1<=a<=5, 1<=b<=2n-1, a+b odd} and edges between (a,b) and (c,d) if and only if |a-b|=|c-d|=1. Then a(n) is the number of independent sets in G_n.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Z. Zhang, Merrifield-Simmons index of generalized Aztec diamond and related graphs, MATCH Commun. Math. Comput. Chem. 56 (2006) 625-636.
Index entries for linear recurrences with constant coefficients, signature (12,-24,5).
FORMULA
G.f.: (1 - 8*x + 5*x^2)/(1 - 12*x + 24*x^2 - 5*x^3).
a(n) = 12*a(n-1) - 24*a(n-2) + 5*a(n-3) for n > 2. - Colin Barker, Jun 07 2020
PROG
(PARI) Vec((1-8*x+5*x^2)/(1-12*x+24*x^2-5*x^3) + O(x^30)) \\ Michel Marcus, Jan 26 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Steve Butler, Jan 25 2015
STATUS
approved