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A143044
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A division-matrix vector Markov: where 8 matrices are projectively divided by a 9th matrix and then iterated in order: ( real part ) Matrices: m0 = Inverse[{{0, I}, {I, 1}}]: 9th; M[0] = {{0, -1}, {-1, -1}}.m0; M[1] = {{1, 0}, {-1, -1}}.m0; M[2] = {{-1, 0}, {-1, -1}}.m0; M[3] = {{0, 1}, {-1, -1}}.m0; M[4] = I*{{0, -1}, {-1, -1}}.m0; M[5] = I*{{1, 0}, {-1, -1}}.m0; M[6] = I*{{-1, 0}, {-1, -1}}.m0; M[7] = I*{{0, 1}, {-1, -1}}.m0.
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1, 1, -3, 0, 0, 4, 6, 5, 18, -23, -24, 24, 17, 88, -7, 145, 5, -376, 376, -236, 654, -755, 34, 3025, -2992, 2992, -5983, -720, -11279, -18015, 48141, -112, 112, -66268, -95338, -85227, -294862, 389049, 381240, -381240, -302671, -1445240, 69609, -2448591, 110613, 6162200, -6162200, 3602996
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| This set of matrices as Moebius transforms and ratio=1/Sqrt[8]
gives a three part fractal. The object is to simulate
a SU(3) level of orthogonality using a division type set of Determinant and -1
matrices.
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FORMULA
| Matrices: m0 = Inverse[{{0, I}, {I, 1}}]: 9th; M[0] = {{0, -1}, {-1, -1}}.m0; M[1] = {{1, 0}, {-1, -1}}.m0; M[2] = {{-1, 0}, {-1, -1}}.m0; M[3] = {{0, 1}, {-1, -1}}.m0; M[4] = I*{{0, -1}, {-1, -1}}.m0; M[5] = I*{{1, 0}, {-1, -1}}.m0; M[6] = I*{{-1, 0}, {-1, -1}}.m0; M[7] = I*{{0, 1}, {-1, -1}}.m0; v(n)=M[Mod[n,7]].v(n-1); a(n)=Realpart(v(n)[[1]]).
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MATHEMATICA
| Clear[M, v, n, a]; m0 = Inverse[{{0, I}, {I, 1}}]; M[0] = {{0, -1}, {-1, -1}}.m0; M[1] = {{1, 0}, {-1, -1}}.m0; M[2] = {{-1, 0}, {-1, -1}}.m0; M[3] = {{0, 1}, {-1, -1}}.m0; M[4] = I*{{0, -1}, {-1, -1}}.m0; M[5] = I*{{1, 0}, {-1, -1}}.m0; M[6] = I*{{-1, 0}, {-1, -1}}.m0; M[7] = I*{{0, 1}, {-1, -1}}.m0; v[0] = {1, 1}; v[n_] := v[n] = M[Mod[n, 7]].v[n - 1]; ar = Table[Re[v[n][[1]]], {n, 0, 50}]
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CROSSREFS
| Sequence in context: A021773 A133109 A130208 * A127775 A092669 A011400
Adjacent sequences: A143041 A143042 A143043 * A143045 A143046 A143047
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KEYWORD
| uned,sign
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Oct 13 2008
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