Search: id:A000913
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%I A000913
%S A000913 0,1,2,12,38,143,490,1768,6268,22610,81620,297160,1086172,3991995,
%T A000913 14731290,54587280,202992808,757398510,2834493948,10637507400,
%U A000913 40023577524,150946230006,570534370692,2160865067312,8199710635816
%N A000913 Number of bond-rooted polyenoids with n edges.
%D A000913 S. J. Cyvin, J. Brunvoll, E. Brendsdal, B. N. Cyvin and E. K. Lloyd, 
               Enumeration of polyene hydrocarbons: a complete mathematical solution, 
               J. Chem. Inf. Comput. Sci., 35 (1995) 743-751
%F A000913 a(n)=(1/4)c(n+2)-(1/2)c(n+1)-(3/4)c((n+1)/2)+(1/2)c((n-1)/4), where c(n)=binomial(2n, 
               n)/(n+1) are the Catalan numbers for n a nonnegative integer and 
               0 otherwise. G.f.=[ -4x+8x^2-sqrt(1-4x)+2xsqrt(1-4x)+3sqrt(1-4x^2)-2sqrt(1-4x^4)]/
               (8x^3). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 19 2004
%p A000913 c:=proc(n) if floor(n)=n then binomial(2*n,n)/(n+1) else 0 fi end:a:=n->
               (1/4)*c(n+2)-(1/2)*c(n+1)-(3/4)*c((n+1)/2)+(1/2)*c((n-1)/4):seq(a(n),
               n=1..27); (Deutsch)
%Y A000913 Sequence in context: A073404 A141208 A035597 this_sequence A026575 A048349 
               A009632
%Y A000913 Adjacent sequences: A000910 A000911 A000912 this_sequence A000914 A000915 
               A000916
%K A000913 nonn
%O A000913 1,3
%A A000913 E. K. Lloyd (E.K.Lloyd(AT)soton.ac.uk)
%E A000913 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 19 2004

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