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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). 0
40, 520, 6800, 89000, 1165000, 15250000, 199625000, 2613125000, 34206250000, 447765625000, 5861328125000, 76725781250000, 1004353515625000, 13147158203125000, 172098535156250000, 2252799072265625000 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 19 2005
STATUS
approved

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Last modified February 24 16:16 EST 2024. Contains 370307 sequences. (Running on oeis4.)