A109115 a(n) = 4*a(n-1) + 3*a(n-2), a(0)=1, a(1)=6.

1, 6, 27, 126, 585, 2718, 12627, 58662, 272529, 1266102, 5881995, 27326286, 126951129, 589783374, 2739986883, 12729297654, 59137151265, 274736498022, 1276357445883, 5929639277598, 27547629448041, 127979435624958

Offset: 0

Author

Emeric Deutsch, Jun 19 2005

Keywords

• nonn
• easy

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_{12}).

Links

• Index entries for linear recurrences with constant coefficients, signature (4, 3).

Programs

Maple

a[0]:=1: a[1]:=6: for n from 2 to 26 do a[n]:=4*a[n-1]+3*a[n-2] od: seq(a[n],n=0..26);

Mathematica

LinearRecurrence[{4,3},{1,6},40] (* Harvey P. Dale, Aug 20 2020 *)

Formula

a(n) = ((sqrt(7) + 4)*(2 + sqrt(7))^n + (sqrt(7) - 4)*(2 - sqrt(7))^n)/(2*sqrt(7)).

G.f.: (1+2z)/(1 - 4z - 3z^2).

a(n) = A015530(n+1)+2*A015530(n). - R. J. Mathar, Jul 26 2022