A109108 a(n) = 10a(n-1) + a(n-2), a(0)=1, a(1)=9.

1, 9, 91, 919, 9281, 93729, 946571, 9559439, 96540961, 974969049, 9846231451, 99437283559, 1004219067041, 10141627953969, 102420498606731, 1034346614021279, 10445886638819521, 105493213002216489

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_1(n)}).

Links

Table of n, a(n) for n=0..17.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (10,1).

Formula

a(n) = (1/2/sqrt(26))((sqrt(26)+4)(5+sqrt(26))^n+(sqrt(26)-4)(5-sqrt(26))^n).

G.f.: (1-z)/(1-10z-z^2).

Maple

a:=n->(1/2/sqrt(26))*((sqrt(26)+4)*(5+sqrt(26))^n+(sqrt(26)-4)*(5-sqrt(26))^n): seq(expand(a(n)), n=0..20);

Mathematica

LinearRecurrence[{10, 1}, {1, 9}, 20] (* Harvey P. Dale, Jan 04 2024 *)

Crossrefs

First differences of A041041.

Sequence in context: A015585 A366393 A242299 * A163456 A318593 A362728

Adjacent sequences: A109105 A109106 A109107 * A109109 A109110 A109111

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 19 2005

Status

approved