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%I #12 Jul 22 2022 09:37:15
%S 1,21,157,707,2353,6405,15106,31998,62349,113641,196119,323401,513149,
%T 787801,1175364,1710268,2434281,3397485,4659313,6289647,8369977,
%U 10994621,14272006,18326010,23297365,29345121,36648171,45406837
%N a(n) = (n+1)*(n+2)*(61*n^4 + 366*n^3 + 845*n^2 + 888*n + 360)/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. 231, # 35).
%H R. P. Stanley, <a href="/A002721/a002721.pdf">Examples of Magic Labelings</a>, Unpublished Notes, 1973 [Cached copy, with permission] See p. 31.
%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 G.f.: (1 + 14*x + 31*x^2 + 14*x^3 + x^4)/(1-x)^7.
%p a:=n->(n+1)*(n+2)*(61*n^4+366*n^3+845*n^2+888*n+360)/720: seq(a(n),n=0..32);
%K nonn,easy
%O 0,2
%A _Emeric Deutsch_, Jun 17 2005
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