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 A114243 a(n) = (n+1)(n+2)^2*(n+3)(n+4)(3n+5)/240. 0
 1, 12, 66, 245, 714, 1764, 3864, 7722, 14355, 25168, 42042, 67431, 104468, 157080, 230112, 329460, 462213, 636804, 863170, 1152921, 1519518, 1978460, 2547480, 3246750, 4099095, 5130216, 6368922, 7847371, 9601320, 11670384, 14098304, 16933224, 20227977 (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 (pp. 167-169, Table 10.5/II/3). LINKS Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1). FORMULA G.f.: (1 + 5*x + 3*x^2)/(1-x)^7. a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - Wesley Ivan Hurt, May 03 2015 MAPLE a:=n->(n+1)*(n+2)^2*(n+3)*(n+4)*(3*n+5)/240: seq(a(n), n=0..35); MATHEMATICA CoefficientList[Series[(1+5x+3x^2)/(1-x)^7, {x, 0, 40}], x]  (* Harvey P. Dale, Feb 19 2011 *) Table[(n + 1) (n + 2)^2 (n + 3) (n + 4) (3 n + 5) / 240, {n, 0, 50}] (* Vincenzo Librandi, May 03 2015 *) PROG (MAGMA) [(n+1)*(n+2)^2*(n+3)*(n+4)*(3*n+5)/240 : n in [0..50]]; // Wesley Ivan Hurt, May 03 2015 CROSSREFS Sequence in context: A007249 A112142 A271870 * A000972 A180392 A161805 Adjacent sequences:  A114240 A114241 A114242 * A114244 A114245 A114246 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Nov 18 2005 STATUS approved

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Last modified April 21 04:56 EDT 2019. Contains 322310 sequences. (Running on oeis4.)