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 A109115 #17 Jun 29 2023 18:55:56
%S A109115 1,6,27,126,585,2718,12627,58662,272529,1266102,5881995,27326286,
%T A109115 126951129,589783374,2739986883,12729297654,59137151265,274736498022,
%U A109115 1276357445883,5929639277598,27547629448041,127979435624958
%N A109115 a(n) = 4*a(n-1) + 3*a(n-2), a(0)=1, a(1)=6.
%C A109115 Kekulé numbers for certain benzenoids.
%D A109115 S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 302, P_{12}).
%H A109115 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4, 3).
%F A109115 a(n) = ((sqrt(7) + 4)*(2 + sqrt(7))^n + (sqrt(7) - 4)*(2 - sqrt(7))^n)/(2*sqrt(7)).
%F A109115 G.f.: (1+2z)/(1 - 4z - 3z^2).
%F A109115 a(n) = A015530(n+1)+2*A015530(n). - _R. J. Mathar_, Jul 26 2022
%p A109115 a[0]:=1: a[1]:=6: for n from 2 to 26 do a[n]:=4*a[n-1]+3*a[n-2] od: seq(a[n],n=0..26);
%t A109115 LinearRecurrence[{4,3},{1,6},40] (* _Harvey P. Dale_, Aug 20 2020 *)
%K A109115 nonn,easy
%O A109115 0,2
%A A109115 _Emeric Deutsch_, Jun 19 2005