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%I #10 Feb 10 2014 01:26:08
%S 2,7,9,16,1,3,2,5,3,2,5,7,4,7,11,18,8,6,14,20,9,16,25,41,5,17,22,39,2,
%T 8,6,14,12,41,53,94,5,19,14,33,19,14,33,47,22,39,61,100,46,34,80,114,
%U 53,94,147,241,29,99,128,227,12,46,34,80,70,239,309,548,29,111,82,193,111
%N M={{0, 1, -1, 1}, {-1, 0, 1, -1}, {1, -1, 0, 1}, {-1, 1, -1, 0}}; a[n_]:=M.a[n-1]; a[0]:={{0, 1, 1, 2}, {1, 1, 2, 3}, {1, 2, 3, 5}, {2, 3, 5, 8}};
%C Group sum matrix of an SO(4) type ( so(4)) of matrix group. Used in four-dimensional electromagnetic theory for a scaled field tensor such that: T(energy density) =s*M.s*MatrixPower[M,-1]/4 where s is the field scale constantSqrt[4*c*hbar^2/(3*e^4)].
%t (* SO(4) Determinant one 4 X 4 Markov sequence *) (* by _Roger L. Bagula_, Sep 09 2004 *) Clear[M, A, x] digits=Floor[21*3/4]; M={{0, 1, -1, 1}, {-1, 0, 1, -1}, {1, -1, 0, 1}, {-1, 1, -1, 0}}; Det[M] A[n_]:=M.A[n-1]; A[0]:={{0, 1, 1, 2}, {1, 1, 2, 3}, {1, 2, 3, 5}, {2, 3, 5, 8}}; (* flattened sequence of 4 X 4 matrices made with an SO(4) Determinant one recurrence*) b=Flatten[Table[M.A[n], {n, 1, digits}]] Floor[Abs[b]] ListPlot[b, PlotJoined->True]
%K nonn
%O 0,1
%A _Roger L. Bagula_, Sep 09 2004
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