%I #9 Sep 06 2017 20:43:49
%S 2,35,1547,67319,3028619,143266535,7089761447,363676815215,
%T 19183734561419,1034368920790919,56759038335333047,
%U 3159418506105987215,177966197529849012647,10125526995020242083599,581051798159881757979599
%N Kekulé numbers for certain benzenoids of trigonal symmetry.
%D S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 313).
%H G. C. Greubel, <a href="/A110697/b110697.txt">Table of n, a(n) for n = 0..550</a>
%F a(n) = 9*binomial(2n, n)^3 - 12*binomial(2n, n)^2 + 6*binomial(2n, n) - 1.
%p 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);
%t 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 *)
%o (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
%K nonn
%O 0,1
%A _Emeric Deutsch_, Aug 03 2005