OFFSET
0,2
COMMENTS
Kekulé numbers for certain benzenoids.
REFERENCES
S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 284, K{Q_2(n)}).
LINKS
Colin Barker, Table of n, a(n) for n = 0..900
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (10,1).
FORMULA
a(n) = (1/2/sqrt(26))((sqrt(26)-1)(5+sqrt(26))^n+(sqrt(26)+1)(5-sqrt(26))^n).
G.f.: (1-6*x) / (1-10*x-x^2).
MAPLE
a:=n->(1/2/sqrt(26))*((sqrt(26)-1)*(5+sqrt(26))^n+(sqrt(26)+1)*(5-sqrt(26))^n): seq(expand(a(n)), n=0..20);
MATHEMATICA
RecurrenceTable[{a[0]==1, a[1]==4, a[n]==10a[n-1]+a[n-2]}, a, {n, 20}] (* or *) LinearRecurrence[{10, 1}, {1, 4}, 50] (* Harvey P. Dale, Dec 03 2017 *)
PROG
(PARI) Vec((1-6*x)/(1-10*x-x^2) + O(x^100)) \\ Colin Barker, Oct 31 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 19 2005
EXTENSIONS
More terms from Colin Barker, Oct 31 2014
STATUS
approved