A107942 a(n) = (n+1)(n+2)^3*(n+3)^3*(n+4)(2n+5)/4320.

1, 28, 300, 1925, 8918, 32928, 102816, 282150, 698775, 1591876, 3383380, 6782139, 12931100, 23609600, 41505024, 70570332, 116486397, 187250700, 293916700, 451511137, 680159634, 1006454240, 1465100000, 2100881250, 2970992115

Offset

0,2

Comments

Kekulé numbers for certain benzenoids.

Dimensions of certain Lie algebra (see Landsberg-Manivel reference for precise definition). - N. J. A. Sloane, Oct 15 2007

Links

Table of n, a(n) for n=0..24.

Antoine Bourget, Amihay Hanany, Dominik Miketa, Quiver origami: discrete gauging and folding, arXiv:2005.05273 [hep-th], 2020. See Eq. (3.50), 1st row in Fig. 8, and top box in Fig. 9.

S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 229).

J. M. Landsberg and L. Manivel, The sextonions and E7 1/2, Adv. Math. 201 (2006), 143-179. [Th. 7.1, case a=0]

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

G.f.: (x+1)*(x^4+17*x^3+48*x^2+17*x+1)/(x-1)^10. - Colin Barker, Sep 20 2012

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10). - Wesley Ivan Hurt, Jun 23 2020

Maple

a:=n->(1/4320)*(n+1)*(n+2)^3*(n+3)^3*(n+4)*(2*n+5): seq(a(n), n=0..30);

Mathematica

Table[(1/4320)(n+1)(n+2)^3(n+3)^3(n+4)(2n+5), {n, 0, 30}] (* Harvey P. Dale, Nov 03 2011 *)

Crossrefs

Sequence in context: A219626 A126662 A156711 * A219172 A334882 A196513

Adjacent sequences: A107939 A107940 A107941 * A107943 A107944 A107945

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 12 2005

Status

approved