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%I #21 Oct 01 2023 11:02:10
%S 4,50,650,8500,111250,1456250,19062500,249531250,3266406250,
%T 42757812500,559707031250,7326660156250,95907226562500,
%U 1255441894531250,16433947753906250,215123168945312500,2815998840332031250
%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 (15,-25).
%F a(n) = 2*((sqrt(5) + 2)((15 + 5*sqrt(5))/2)^(n-1) + (sqrt(5) - 2)*((15 - 5*sqrt(5))/2)^(n-1))/sqrt(5).
%F From _Colin Barker_, Aug 30 2013: (Start)
%F a(n) = 15*a(n-1) - 25*a(n-2).
%F G.f.: -2*x*(5*x-2) / (25*x^2 - 15*x + 1). (End)
%p a:=2*((sqrt(5)+2)*((15+5*sqrt(5))/2)^(n-1)+(sqrt(5)-2)*((15-5*sqrt(5))/2)^(n-1))/sqrt(5): seq(expand(a(n)),n=1..20);
%t LinearRecurrence[{15,-25},{4,50},20] (* _Harvey P. Dale_, Oct 01 2023 *)
%K nonn
%O 1,1
%A _Emeric Deutsch_, Nov 30 2005