A109105 - OEIS

A109105

a(n) = (8*sqrt(5)/25)((sqrt(5) + 2)((15 + 5*sqrt(5))/2)^n + (sqrt(5) - 2)((15 - 5*sqrt(5))/2)^n).

40, 520, 6800, 89000, 1165000, 15250000, 199625000, 2613125000, 34206250000, 447765625000, 5861328125000, 76725781250000, 1004353515625000, 13147158203125000, 172098535156250000, 2252799072265625000

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OFFSET

1,1

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. 215, K{S_m}).

LINKS

Table of n, a(n) for n=1..16.

Index entries for linear recurrences with constant coefficients, signature (15,-25).

FORMULA

G.f.: 40*z(1-2*z)/(1 - 15*z + 25*z^2).

Let b(n) = 5^n*A001906(n+1) = 1, 15, 200, 2625,... (n>=0) then a(n) = 40*[b(n)-2*b(n-1)]. - R. J. Mathar, Jul 22 2022

MAPLE

a:=n->(8/5/sqrt(5))*((sqrt(5)+2)*((15+5*sqrt(5))/2)^n+(sqrt(5)-2)*((15-5*sqrt(5))/2)^n): seq(expand(a(n)), n=1..19);

CROSSREFS

Sequence in context: A223162 A069079 A093744 * A269692 A247409 A107419

Adjacent sequences: A109102 A109103 A109104 * A109106 A109107 A109108

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Jun 19 2005

STATUS

approved