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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
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
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.)