A109114 a(n) = 5*a(n-1) - 3*a(n-2), a(0)=1, a(1)=6.

1, 6, 27, 117, 504, 2169, 9333, 40158, 172791, 743481, 3199032, 13764717, 59226489, 254838294, 1096512003, 4718045133, 20300689656, 87349312881, 375844495437, 1617174538542, 6958339206399, 29940172416369, 128825844462648

Offset: 0

Author

Emeric Deutsch, Jun 19 2005

Keywords

• nonn

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. 302, P_{11}).

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-3).

Programs

Maple

a[0]:=1: a[1]:=6: for n from 2 to 26 do a[n]:=5*a[n-1]-3*a[n-2] od: seq(a[n],n=0..26);

Mathematica

LinearRecurrence[{5,-3},{1,6},30] (* Harvey P. Dale, Dec 03 2012 *)

Formula

a(n) = ((sqrt(13) + 7)*((5 + sqrt(13))/2)^n + (sqrt(13) - 7)*((5 - sqrt(13))/2)^n)/(2*sqrt(13)).

G.f.: (1+z)/(1 - 5z + 3z^2).

a(n) = A116415(n)+A116415(n-1). - R. J. Mathar, Jul 26 2022