This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A109114 #20 Jul 26 2022 14:24:06
%S A109114 1,6,27,117,504,2169,9333,40158,172791,743481,3199032,13764717,
%T A109114 59226489,254838294,1096512003,4718045133,20300689656,87349312881,
%U A109114 375844495437,1617174538542,6958339206399,29940172416369,128825844462648
%N A109114 a(n) = 5*a(n-1) - 3*a(n-2), a(0)=1, a(1)=6.
%C A109114 Kekulé numbers for certain benzenoids.
%D A109114 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 A109114 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-3).
%F A109114 a(n) = ((sqrt(13) + 7)*((5 + sqrt(13))/2)^n + (sqrt(13) - 7)*((5 - sqrt(13))/2)^n)/(2*sqrt(13)).
%F A109114 G.f.: (1+z)/(1 - 5z + 3z^2).
%F A109114 a(n) = A116415(n)+A116415(n-1). - _R. J. Mathar_, Jul 26 2022
%p A109114 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 A109114 LinearRecurrence[{5,-3},{1,6},30] (* _Harvey P. Dale_, Dec 03 2012 *)
%K A109114 nonn
%O A109114 0,2
%A A109114 _Emeric Deutsch_, Jun 19 2005