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Kekulé numbers for certain benzenoids of trigonal symmetry.
1

%I #9 Sep 06 2017 20:42:56

%S 1,28,1456,66178,3014128,143076778,7087202890,363641489638,

%T 19183237689328,1034361829223578,56758935931548706,

%U 3159417013205183638,177966175592478108106,10125526670502832205398,581051793331857091649398

%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="/A110696/b110696.txt">Table of n, a(n) for n = 0..550</a>

%F a(n) = 9*binomial(2n, n)^3 - 15*binomial(2n, n)^2 + 9*binomial(2n, n) - 2.

%p a:=n->9*binomial(2*n,n)^3-15*binomial(2*n,n)^2+9*binomial(2*n,n)-2; seq(a(n),n=0..16);

%t Table[9*Binomial[2*n, n]^3 - 15*Binomial[2*n, n]^2 + 9*Binomial[2*n, n] - 2, {n,0,50}] (* _G. C. Greubel_, Sep 06 2017 *)

%o (PARI) for(n=0,25, print1(9*binomial(2n, n)^3 - 15*binomial(2n, n)^2 + 9*binomial(2n, n) - 2, ", ")) \\ _G. C. Greubel_, Sep 06 2017

%K nonn

%O 0,2

%A _Emeric Deutsch_, Aug 03 2005