A109120 a(n) = 10*(n+1)^3*(n+2)*(5*n+7)^2.

980, 34560, 312120, 1548800, 5467500, 15482880, 37565360, 81285120, 161036100, 297440000, 518930280, 863516160, 1380726620, 2133734400, 3201660000, 4682055680, 6693569460, 9378789120, 12907266200, 17478720000, 23326421580, 30720757760, 39972975120, 51439104000

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