A108680 Kekulé numbers for certain benzenoids.

1, 18, 140, 700, 2646, 8232, 22176, 53460, 117975, 242242, 468468, 861224, 1516060, 2570400, 4217088, 6720984, 10439037, 15844290, 23554300, 34364484, 49286930, 69595240, 96876000, 133087500, 180626355, 242402706, 321924708, 423393040

Offset

0,2

References

S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 232, # 3).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

G.f.: (1 + 9*x + 14*x^2 + 4*x^3)/(1 - x)^9.

a(n) = (n + 1)*(n + 2)^3*(n + 3)^2*(n + 4)*(n + 5)/1440 (from Maple section).

Sum_{n>=0} 1/a(n) = -240*zeta(3) + (400/3)*Pi^2 - 18475/18. - Jaume Oliver Lafont, Jul 10 2017

Sum_{n>=0} (-1)^n/a(n) = 4480*log(2)/3 + 180*zeta(3) - 20*Pi^2/3 - 21325/18. - Amiram Eldar, May 29 2022

Maple

a:=n->(n+1)*(n+2)^3*(n+3)^2*(n+4)*(n+5)/1440: seq(a(n), n=0..30);

Mathematica

CoefficientList[Series[(1 + 9 x + 14 x^2 + 4 x^3) / (1 - x)^9, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 11 2017 *)

Prog

(Magma) [(n+1)*(n+2)^3*(n+3)^2*(n+4)*(n+5)/1440: n in [0..30]]; // Vincenzo Librandi, Jul 11 2017

Crossrefs

Sequence in context: A087115 A163707 A212154 * A204273 A081074 A299062

Adjacent sequences: A108677 A108678 A108679 * A108681 A108682 A108683

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 18 2005

Status

approved