A114241 a(n) = (n+1)*(n+2)*(n+3)*(11*n^2 + 29*n + 20)/120.

1, 12, 61, 206, 546, 1232, 2478, 4572, 7887, 12892, 20163, 30394, 44408, 63168, 87788, 119544, 159885, 210444, 273049, 349734, 442750, 554576, 687930, 845780, 1031355, 1248156, 1499967, 1790866, 2125236, 2507776, 2943512, 3437808

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

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

From Chai Wah Wu, Nov 11 2018: (Start)

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 5.

G.f.: (4*x^2 + 6*x + 1)/(x - 1)^6. (End)

E.g.f.: (120 + 1320*x + 2280*x^2 + 1160*x^3 + 205*x^4 + 11*x^5)*exp(x)/5!. - G. C. Greubel, Nov 11 2018

Maple

a:=n->(n+1)*(n+2)*(n+3)*(11*n^2+29*n+20)/120: seq(a(n), n=0..38);

Mathematica

Table[Binomial[n+3, 3]*(11*n^2 +29*n +20)/20, {n, 0, 20}] (* G. C. Greubel, Nov 11 2018 *)

Prog

(PARI) vector(35, n, n--; binomial(n+3, 3)*(11*n^2 +29*n +20)/20) \\ G. C. Greubel, Nov 11 2018
(Magma) [Binomial(n+3, 3)*(11*n^2 +29*n +20)/20: n in [0..35]]; // G. C. Greubel, Nov 11 2018

Crossrefs

Sequence in context: A044531 A304205 A240002 * A127766 A005173 A196144

Adjacent sequences: A114238 A114239 A114240 * A114242 A114243 A114244

Keyword

nonn,easy

Author

Emeric Deutsch, Nov 18 2005

Status

approved