

A108680


KekulĂ© numbers for certain benzenoids.


1



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
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OFFSET

0,2


REFERENCES

S. J. Cyvin and I. Gutman, KekulĂ© 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


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 20217


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



