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Search: id:A098017
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| A098017 |
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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}}; |
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+0
1
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| 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; listen)
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OFFSET
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0,1
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COMMENT
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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)]
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MATHEMATICA
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(* SO(4) Determinant one 4 X 4 Markov sequence *) (* by Roger L. Bagula 9 Sept 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]
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CROSSREFS
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Sequence in context: A102994 A085544 A106352 this_sequence A020894 A022113 A041643
Adjacent sequences: A098014 A098015 A098016 this_sequence A098018 A098019 A098020
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 09 2004
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