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A143050
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A division-matrix vector Markov: where 8 matrices are projectively divided by a 9th matrix and then iterated in order: ( Imaginary 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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0
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0, -1, 0, 3, -3, 2, -5, 6, 0, -24, 23, -23, 47, 7, 88, 143, -376, -5, 5, 514, 755, 654, 2304, -2992, -3025, 3025, 2271, 11279, -720, 18847, -112, -48141, 48141, -29182, 85227, -95338, 8960, 381240, -389049, 389049, -761329, -69609, -1445240, -2268369, 6162200, -110613, 110613, -8541182, -12033565
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OFFSET
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1,4
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COMMENTS
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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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LINKS
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Table of n, a(n) for n=1..49.
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FORMULA
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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)=Imaginarypart(v(n)[[1]]).
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MATHEMATICA
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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}]; ai = Table[Im[v[n][[1]]], {n, 0, 50}]
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CROSSREFS
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Sequence in context: A110897 A116644 A166462 * A214919 A070163 A083343
Adjacent sequences: A143047 A143048 A143049 * A143051 A143052 A143053
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KEYWORD
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uned,sign
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AUTHOR
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Roger L. Bagula, Oct 13 2008
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STATUS
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approved
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