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 A098017 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}}; 0
 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, 8, 6, 14, 12, 41, 53, 94, 5, 19, 14, 33, 19, 14, 33, 47, 22, 39, 61, 100, 46, 34, 80, 114, 53, 94, 147, 241, 29, 99, 128, 227, 12, 46, 34, 80, 70, 239, 309, 548, 29, 111, 82, 193, 111 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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)]. LINKS Table of n, a(n) for n=0..72. MATHEMATICA (* 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] CROSSREFS Sequence in context: A085544 A154789 A106352 * A225675 A185869 A020894 Adjacent sequences: A098014 A098015 A098016 * A098018 A098019 A098020 KEYWORD nonn AUTHOR Roger L. Bagula, Sep 09 2004 STATUS approved

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Last modified July 20 17:24 EDT 2024. Contains 374459 sequences. (Running on oeis4.)