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%I #10 Jan 05 2022 12:21:59
%S 1,18,123,523,1673,4424,10206,21246,40821,73546,125697,205569,323869,
%T 494144,733244,1061820,1504857,2092242,2859367,3847767,5105793,
%U 6689320,8662490,11098490,14080365,17701866,22068333,27297613,33521013,40884288
%N a(n) = (n+1)(n+2)(n+3)(35n^3 + 153n^2 + 232n + 120)/720.
%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. 230).
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).
%F From _R. J. Mathar_, Apr 07 2008: (Start)
%F O.g.f.: -(1 + 11x + 18x^2 + 5x^3)/(-1+x)^7.
%F a(n) = A107962(n) - A107962(n-1). (End)
%p a:=n->(1/720)*(n+1)*(n+2)*(n+3)*(35*n^3+153*n^2+232*n+120): seq(a(n),n=0..35);
%t Table[(n+1)(n+2)(n+3)(35n^3+153n^2+232n+120)/720,{n,0,30}] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,18,123,523,1673,4424,10206},30] (* _Harvey P. Dale_, Jan 05 2022 *)
%K nonn,easy
%O 0,2
%A _Emeric Deutsch_, Jun 12 2005
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