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 A114241 a(n) = (n+1)*(n+2)*(n+3)*(11*n^2 + 29*n + 20)/120. 1
 1, 12, 61, 206, 546, 1232, 2478, 4572, 7887, 12892, 20163, 30394, 44408, 63168, 87788, 119544, 159885, 210444, 273049, 349734, 442750, 554576, 687930, 845780, 1031355, 1248156, 1499967, 1790866, 2125236, 2507776, 2943512, 3437808 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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. 168). LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). FORMULA From Chai Wah Wu, Nov 11 2018: (Start) a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 5. G.f.: (4*x^2 + 6*x + 1)/(x - 1)^6. (End) E.g.f.: (120 + 1320*x + 2280*x^2 + 1160*x^3 + 205*x^4 + 11*x^5)*exp(x)/5!. - G. C. Greubel, Nov 11 2018 MAPLE a:=n->(n+1)*(n+2)*(n+3)*(11*n^2+29*n+20)/120: seq(a(n), n=0..38); MATHEMATICA Table[Binomial[n+3, 3]*(11*n^2 +29*n +20)/20, {n, 0, 20}] (* G. C. Greubel, Nov 11 2018 *) PROG (PARI) vector(35, n, n--; binomial(n+3, 3)*(11*n^2 +29*n +20)/20) \\ G. C. Greubel, Nov 11 2018 (MAGMA) [Binomial(n+3, 3)*(11*n^2 +29*n +20)/20: n in [0..35]]; // G. C. Greubel, Nov 11 2018 CROSSREFS Sequence in context: A044531 A304205 A240002 * A127766 A005173 A196144 Adjacent sequences:  A114238 A114239 A114240 * A114242 A114243 A114244 KEYWORD nonn AUTHOR Emeric Deutsch, Nov 18 2005 STATUS approved

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Last modified May 24 11:23 EDT 2019. Contains 323529 sequences. (Running on oeis4.)