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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

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);

CROSSREFS

First differences of A041041.

Sequence in context: A014992 A015585 A242299 * A163456 A176735 A286786

Adjacent sequences:  A109105 A109106 A109107 * A109109 A109110 A109111

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Jun 19 2005

STATUS

approved

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Last modified August 18 08:18 EDT 2017. Contains 290685 sequences.