The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A107942 a(n) = (n+1)(n+2)^3*(n+3)^3*(n+4)(2n+5)/4320. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 12 2005
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 15 19:43 EDT 2024. Contains 373410 sequences. (Running on oeis4.)