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A109108
a(n) = 10a(n-1) + a(n-2), a(0)=1, a(1)=9.
0
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)}).
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 19 2005
STATUS
approved