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%I #23 Jul 24 2022 10:59:39
%S 3,20,136,928,6336,43264,295424,2017280,13774848,94060544,642285568,
%T 4385800192,29948116992,204498534400,1396403339264,9535238438912,
%U 65110680797184,444603538866176,3035942864551936,20730714605486080
%N 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. 205).
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-8).
%F a(n) = ((4+sqrt(8))^(n+1) + (4-sqrt(8))^(n+1))/16.
%F a(n) = 8*a(n-1) - 8*a(n-2). - _Colin Barker_, Aug 30 2013
%F G.f.: -x*(4*x-3) / (8*x^2 - 8*x + 1). - _Colin Barker_, Aug 30 2013
%F a(n)= 3*A057084(n-1) - 4*A057084(n-2). - _R. J. Mathar_, Aug 30 2013
%F a(n) = A007052(n+1)*2^(n-1). - _R. J. Mathar_, Jul 24 2022
%p a:=((4+sqrt(8))^(n+1)+(4-sqrt(8))^(n+1))/16: seq(expand(a(n)),n=1..23);
%K nonn,easy
%O 1,1
%A _Emeric Deutsch_, Nov 30 2005
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