Search: id:A102081
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%I A102081
%S A102081 5,4,9,11,20,29,49,76,125,199,324,521,845,1364,2209,3571,5780,9349,
%T A102081 15129,24476,39605,64079,103684,167761,271445,439204,710649,1149851,
%U A102081 1860500,3010349,4870849,7881196,12752045,20633239,33385284,54018521
%N A102081 Number of perfect matchings in the C_n X P_2 graph (C_n is the cycle 
               graph on n vertices and P_2 is the path graph on 2 vertices).
%C A102081 a(n)=A102079(n,n).
%C A102081 Apart from initial term, identical to A068397. - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), 
               Jun 03 2006
%D A102081 H. Hosoya and A. Motoyama, An effective algorithm for obtaining polynomials 
               for dimer statistics. Application of operator technique on the topological 
               index to two- and three-dimensional rectangular and torus lattices, 
               J. Math. Physics 26 (1985) 157-167 (eq. (21) and Table IV).
%F A102081 G.f.=z^2*(5-z-5z^2-z^3)/[(1+z)(1-2z+z^3)]. a(n)=a(n-1)+2a(n-2)-a(n-3)-a(n-4) 
               for n >= 6.
%e A102081 Example: a(3)=4 because in the graph with vertex set {A,B,C,A',B',C'} 
               and edge set {AB,AC,BC, A'B',A'C',B'C',AA',BB',CC'} we have the following 
               perfect matchings: {AA',BC,B'C'},{BB',AC,A'C'}, {CC',AB,A'B'}} and 
               {AA',BB',CC'}.
%p A102081 a[2]:=5: a[3]:=4: a[4]:=9: a[5]:=11: for n from 6 to 45 do a[n]:=a[n-1]+2*a[n-2]-a[n-3]-a[n-4] 
               od:seq(a[n],n=2..40);
%Y A102081 Cf. A102079.
%Y A102081 Sequence in context: A057763 A054508 A110617 this_sequence A068397 A022344 
               A046588
%Y A102081 Adjacent sequences: A102078 A102079 A102080 this_sequence A102082 A102083 
               A102084
%K A102081 nonn
%O A102081 2,1
%A A102081 Emeric Deutsch (deutsch(AT)duke.poly.eduandgessel(AT)brandeis.edu), Dec 
               29 2004

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