Search: id:A129757
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%I A129757
%S A129757 1,1,3,5,12,25,54,113,235,481,980,1985,4007,8065,16204,32513,65175,
%T A129757 130561,261421,523265,1047129,2095105,4191409,8384513,16771425,33546241,
%U A129757 67097280,134201345,268412287,536838145,1073695485,2147418113
%N A129757 Maximum genus of fixed edge 2^m-1 binary state graph with 2*m+1 states: 
               Vertices(n)=Floor[2^(n/2)]; Faces(n)=Floor[2^[m-n/2]; Edges(n)=Vertices(n)+Faces(n)-2+2*g=2^m-1; 
               solved for g at the central point m.
%C A129757 The idea was to get a binary graph system of vertices, edges and faces 
               that had a genus near the exceptional group sequence dimension. It 
               is a form of combinatorial optimization. The object was to get an 
               idea of what higher dimenional exceptional group dimensions would 
               look like if they existed.
%F A129757 a(n) =Ceiling[Flatten[Table[N[Flatten[g /. Solve[2*Floor[2^(n/2)] - 2 
               + 2*g - (2^n - 1) == 0, g]]], {n, 1, 32}]]]
%e A129757 Exceptal group dimension to output:
%e A129757 14->12->G2
%e A129757 24 ->25->A4
%e A129757 52 ->54->F4
%e A129757 133->113->E7
%e A129757 248->235->E8
%e A129757 484->481->E9
%e A129757 (?)->980->E10
%e A129757 Example 21 state system 2^10:
%e A129757 a = Table[Flatten[{n/20, N[Flatten[g /. Solve[v[n] + f[n] - 2 + 2*g - 
               1023 == 0, g]]/480.5]}], {n, 0, 20}];
%e A129757 ListPlot[a, PlotJoined -> True]
%e A129757 The normalized to one Plot has the form of dimension for a multifractal 
               system.
%t A129757 Ceiling[Flatten[Table[N[Flatten[g /. Solve[2*Floor[2^(n/2)] - 2 + 2*g 
               - (2^n - 1) == 0, g]]], {n, 1, 32}]]]
%Y A129757 Sequence in context: A090345 A151524 A030270 this_sequence A135019 A141685 
               A017921
%Y A129757 Adjacent sequences: A129754 A129755 A129756 this_sequence A129758 A129759 
               A129760
%K A129757 nonn,uned
%O A129757 1,3
%A A129757 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 15 2007

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