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%I #20 Jul 26 2022 14:24:06
%S 1,6,27,117,504,2169,9333,40158,172791,743481,3199032,13764717,
%T 59226489,254838294,1096512003,4718045133,20300689656,87349312881,
%U 375844495437,1617174538542,6958339206399,29940172416369,128825844462648
%N a(n) = 5*a(n-1) - 3*a(n-2), a(0)=1, a(1)=6.
%C Kekulé numbers for certain benzenoids.
%D S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 302, P_{11}).
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-3).
%F a(n) = ((sqrt(13) + 7)*((5 + sqrt(13))/2)^n + (sqrt(13) - 7)*((5 - sqrt(13))/2)^n)/(2*sqrt(13)).
%F G.f.: (1+z)/(1 - 5z + 3z^2).
%F a(n) = A116415(n)+A116415(n-1). - _R. J. Mathar_, Jul 26 2022
%p a[0]:=1: a[1]:=6: for n from 2 to 26 do a[n]:=5*a[n-1]-3*a[n-2] od: seq(a[n],n=0..26);
%t LinearRecurrence[{5,-3},{1,6},30] (* _Harvey P. Dale_, Dec 03 2012 *)
%K nonn
%O 0,2
%A _Emeric Deutsch_, Jun 19 2005