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 A109106 a(n) = (1/sqrt(5))((sqrt(5) + 1)((15 + 5sqrt(5))/2)^(n-1) + (sqrt(5) - 1)((15 - 5sqrt(5))/2)^(n-1)). 4
 2, 20, 250, 3250, 42500, 556250, 7281250, 95312500, 1247656250, 16332031250, 213789062500, 2798535156250, 36633300781250, 479536132812500, 6277209472656250, 82169738769531250, 1075615844726562500 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS KekulĂ© numbers for certain benzenoids. REFERENCES S. J. Cyvin and I. Gutman, KekulĂ© structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 215, K{T_m}). LINKS FORMULA G.f.: 2z(1-5z)/(1 - 15z + 25z^2). From Johannes W. Meijer, Jul 01 2010: (Start) a(n) = A178381(4*n+2). Limit(a(n+k)/a(k), k=infinity) = (A020876(2*n) + 5*A039717(2*n-2)*sqrt(5))/2. Limit(A020876(2*n)/(5*A039717(2*n-2)), n=infinity) = sqrt(5). (End) a(n) = 2*5^(n-1)*Fibonacci(2*n-1). - Ehren Metcalfe, Apr 21 2018 MAPLE a:=n->(1/sqrt(5))*((sqrt(5)+1)*((15+5*sqrt(5))/2)^(n-1)+(sqrt(5)-1)*((15-5*sqrt(5))/2)^(n-1)): seq(expand(a(n)), n=1..19); CROSSREFS Cf. A179135. - Johannes W. Meijer, Jul 01 2010 Sequence in context: A296660 A197898 A293471 * A099976 A195157 A207151 Adjacent sequences:  A109103 A109104 A109105 * A109107 A109108 A109109 KEYWORD nonn AUTHOR Emeric Deutsch, Jun 19 2005 STATUS approved

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Last modified September 20 12:37 EDT 2019. Contains 327237 sequences. (Running on oeis4.)