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Search: id:A116560
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| A116560 |
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Sequentually switched Markov of six 2 X 2 matrices based on the Anharmonic group that gives a chaotic vector output. |
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1
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| 0, 1, 1, 0, 0, 1, 1, 1, 2, 1, 1, 2, 2, 3, 5, 2, 2, 5, 5, 7, 12, 5, 5, 12, 12, 17, 29, 12, 12, 29, 29, 41, 70, 29, 29, 70, 70
(list; graph; listen)
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OFFSET
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0,9
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COMMENT
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This group is isomorphic ( can be mapped to ) with the SL[2,2] as a representation of S3, even permutation group. Second element is alternating here and gives a cycle with the first: b = Table[v[n][[2]], {n, 0, 36}] {1, 1, 1, 1, -1, -1, -1, -2, -1, -2, 3, 3, 3, 5, 3, 5, -7, -7, -7, -12, -7, -12, 17, 17, 17, 29, 17, 29, -41, -41, -41, -70, -41, -70, 99, 99, 99}
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REFERENCES
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Blyth and Robonson,Essential Student Algebra, V5,Groups,J.W. Arrowsmith, Bristol,1986, page 9
McKean and Moll, Elliptic Curves,Cambridge, New York,1997, pages 13,169-171
Andree,Selections from Modern Algebra,Henry Holt and Co, New york,1958, pages 86,91
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FORMULA
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M1 = {{1, 0}, {0, 1}}; M2 = {{0, 1}, {-1, 1}}; M3 = {{-1, 1}, {1, 0}}; M4 = {{1, 0}, {1, -1}}; M5 = {{1, -1}, {0, 1}}; M6 = {{0, 1}, {1, 0}}; M[n_] = If[Mod[n, 6] == 0, M1, If[Mod[n, 6] == 1, M2, If[ Mod[n, 6] == 3, M3, If[Mod[n, 6] == 4, M4, If[Mod[n, 6] == 5, M5, M6]]]]]; v[0] = {0, 1}; v[n_] := v[n] = M[n].v[n - 1] a(n) =v[n][[[1]]
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MATHEMATICA
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M1 = {{1, 0}, {0, 1}}; M2 = {{0, 1}, {-1, 1}}; M3 = {{-1, 1}, {1, 0}}; M4 = {{1, 0}, {1, -1}}; M5 = {{1, -1}, {0, 1}}; M6 = {{0, 1}, {1, 0}}; M[n_] = If[Mod[n, 6] == 0, M1, If[Mod[n, 6] == 1, M2, If[ Mod[n, 6] == 3, M3, If[Mod[n, 6] == 4, M4, If[Mod[n, 6] == 5, M5, M6]]]]]; v[0] = {0, 1}; v[n_] := v[n] = M[n].v[n - 1] a = Table[Abs[v[n][[1]]], {n, 0, 36}]
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CROSSREFS
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Sequence in context: A100480 A113297 A119985 this_sequence A103784 A045870 A036863
Adjacent sequences: A116557 A116558 A116559 this_sequence A116561 A116562 A116563
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KEYWORD
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nonn,uned,probation,obsc
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 17 2006
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