A110695 Kekulé numbers for certain benzenoids of trigonal symmetry.

1, 9, 341, 14859, 671509, 31816259, 1575219491, 80813149559, 4262996933909, 229858972288659, 12613108252122091, 702092835479959559, 39548041458039952291, 2250117073947022121799, 129122621276859925669799

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 (see p. 313).

Links

G. C. Greubel, Table of n, a(n) for n = 0..555

Formula

a(n) = (2*binomial(2*n,n) - 1)*(binomial(2*n,n)^2 - binomial(2*n,n) + 1).

G.f.: 3/sqrt(1 - 4*x) - 1/(1 - x) + (8*EllipticK((1/2)*(1 - sqrt(1 - 64*x)))^2)/Pi^2 - (6*EllipticK(16*x))/Pi. - G. C. Greubel, Sep 06 2017

Maple

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A098650 A354689 A098652 * A157589 A055601 A225328

Adjacent sequences: A110692 A110693 A110694 * A110696 A110697 A110698

Keyword

nonn,easy

Author

Emeric Deutsch, Aug 03 2005

Status

approved