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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 (list; graph; refs; listen; history; text; internal format)
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
Tanya Khovanova, Recursive Sequences
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

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Last modified July 23 15:54 EDT 2024. Contains 374552 sequences. (Running on oeis4.)