A110697 Kekulé numbers for certain benzenoids of trigonal symmetry.

2, 35, 1547, 67319, 3028619, 143266535, 7089761447, 363676815215, 19183734561419, 1034368920790919, 56759038335333047, 3159418506105987215, 177966197529849012647, 10125526995020242083599, 581051798159881757979599

Offset

0,1

References

S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 313).

Links

G. C. Greubel, Table of n, a(n) for n = 0..550

Formula

a(n) = 9*binomial(2n, n)^3 - 12*binomial(2n, n)^2 + 6*binomial(2n, n) - 1.

Maple

a:=n->9*binomial(2*n, n)^3-12*binomial(2*n, n)^2+6*binomial(2*n, n)-1; seq(a(n), n=0..16);

Mathematica

Table[9*Binomial[2*n, n]^3 - 12*Binomial[2*n, n]^2 + 6*Binomial[2*n, n] - 1, {n, 0, 50}] (* G. C. Greubel, Sep 06 2017 *)

Prog

(PARI) for(n=0, 25, print1(9*binomial(2n, n)^3 - 12*binomial(2n, n)^2 + 6*binomial(2n, n) - 1, ", ")) \\ G. C. Greubel, Sep 06 2017

Crossrefs

Sequence in context: A191807 A245052 A266316 * A322514 A132100 A327129

Adjacent sequences: A110694 A110695 A110696 * A110698 A110699 A110700

Keyword

nonn

Author

Emeric Deutsch, Aug 03 2005

Status

approved