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

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. 284, K{Q_1(n)}).

Links

• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (10,1).

Crossrefs

First differences of A041041.

Programs

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 *)

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).