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%I #15 Jul 22 2022 09:29:52
%S 2,13,72,393,2142,11673,63612,346653,1889082,10294533,56099952,
%T 305716113,1665996822,9078832593,49475005092,269613532773,
%U 1469256181362,8006696489853,43632410395032,237774372900633,1295749006218702
%N a(n) = 6*a(n-1) - 3*a(n-2), a(0)=2, a(1)=13.
%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_{14}).
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-3).
%F a(n) = (1/(2*sqrt(6)))*((2*sqrt(6) + 7)*(3 + sqrt(6))^n + (2*sqrt(6) - 7)*(3 - sqrt(6))^n).
%F G.f.: (2+z)/(1 - 6z + 3z^2).
%F a(n) = 2*A138395(n) + A138395(n-1). - _R. J. Mathar_, Jul 22 2022
%p a[0]:=2:a[1]:=13: for n from 2 to 24 do a[n]:=6*a[n-1]-3*a[n-2] od: seq(a[n],n=0..24);
%t LinearRecurrence[{6,-3},{2,13},30] (* _Harvey P. Dale_, Dec 15 2014 *)
%K nonn,easy
%O 0,1
%A _Emeric Deutsch_, Jun 19 2005
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