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 A109120 a(n) = 10*(n+1)^3*(n+2)*(5*n+7)^2. 1
 980, 34560, 312120, 1548800, 5467500, 15482880, 37565360, 81285120, 161036100, 297440000, 518930280, 863516160, 1380726620, 2133734400, 3201660000, 4682055680, 6693569460, 9378789120, 12907266200, 17478720000, 23326421580, 30720757760, 39972975120, 51439104000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 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. 311). LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1). FORMULA G.f.: 20*(49 + 1385*z + 4539*z^2 + 2771*z^3 + 256*z^4)/(1-z)^7. E.g.f.: 10*(98 + 3358*x + 12199*x^2 + 11919*x^3 + 4199*x^4 + 570*x^5 + 25*x^6)*exp(x). - G. C. Greubel, Feb 09 2020 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, Aug 19 2022 MAPLE a:=n->10*(n+1)^3*(n+2)*(5*n+7)^2: seq(a(n), n=0..30); MATHEMATICA Table[10(n+1)^3(n+2)(5n+7)^2, {n, 0, 30}] LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {980, 34560, 312120, 1548800, 5467500, 15482880, 37565360}, 30] (* Harvey P. Dale, Jan 20 2024 *) PROG (PARI) vector(31, n, my(m=n-1); 10*(m+1)^3*(m+2)*(5*m+7)^2) \\ G. C. Greubel, Feb 09 2020 (Magma) [10*(n+1)^3*(n+2)*(5*n+7)^2: n in [0..30]]; // G. C. Greubel, Feb 09 2020 (Sage) [10*(n+1)^3*(n+2)*(5*n+7)^2 for n in (0..30)] # G. C. Greubel, Feb 09 2020 (GAP) List([0..30], n-> 10*(n+1)^3*(n+2)*(5*n+7)^2 ); # G. C. Greubel, Feb 09 2020 CROSSREFS Sequence in context: A091080 A157515 A188337 * A128483 A056937 A251839 Adjacent sequences: A109117 A109118 A109119 * A109121 A109122 A109123 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jun 19 2005 STATUS approved

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Last modified June 17 07:23 EDT 2024. Contains 373433 sequences. (Running on oeis4.)