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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 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

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