A114240 a(n) = (n+1)*(n+2)^2*(n+3)*(7*n^2 + 23*n + 20)/240.

1, 15, 94, 380, 1176, 3038, 6888, 14148, 26895, 48037, 81510, 132496, 207662, 315420, 466208, 672792, 950589, 1318011, 1796830, 2412564, 3194884, 4178042, 5401320, 6909500, 8753355, 10990161, 13684230, 16907464, 20739930, 25270456

Offset

0,2

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. 168).

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

G.f.: -(2*x^3+10*x^2+8*x+1)/(x-1)^7. - Alois P. Heinz, Feb 27 2015

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, Jun 26 2025

Maple

a:=n->(n+1)*(n+2)^2*(n+3)*(7*n^2+23*n+20)/240: seq(a(n), n=0..33);

Mathematica

LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 15, 94, 380, 1176, 3038, 6888}, 50] (* or *)
A114240[n_] := (n + 1)*(n + 2)^2*(n + 3)*((7*n + 23)*n + 20)/240;
Array[A114240, 50, 0] (* Paolo Xausa, Jun 27 2025 *)

Crossrefs

Sequence in context: A125325 A126483 A226766 * A189657 A190274 A374808

Adjacent sequences: A114237 A114238 A114239 * A114241 A114242 A114243

Keyword

nonn,easy

Author

Emeric Deutsch, Nov 18 2005

Status

approved