OFFSET
1,1
REFERENCES
S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 205).
LINKS
Index entries for linear recurrences with constant coefficients, signature (27,-108,108).
FORMULA
a(n) = (3^(n+1) + (12 + 6*sqrt(3))^(n+1)/4 + (12 - 6*sqrt(3))^(n+1)/4)/27.
From Colin Barker, Aug 30 2013: (Start)
a(n) = 27*a(n-1) - 108*a(n-2) + 108*a(n-3).
G.f.: -x*(36*x^2 - 30*x + 5) / ((3*x-1)*(36*x^2 - 24*x + 1)). (End)
9*a(n) = 3^n+ 6^n*A001075(n+1). - R. J. Mathar, Jul 22 2022
MAPLE
a:=n->(3^(n+1)+(12+6*sqrt(3))^(n+1)/4+(12-6*sqrt(3))^(n+1)/4)/27: seq(expand(a(n)), n=1..18);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 30 2005
STATUS
approved