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A116560
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Sequentially 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, 99, 169, 70, 70, 169, 169, 239, 408, 169, 169, 408, 408, 577, 985, 408, 408, 985, 985, 1393, 2378, 985, 985, 2378, 2378
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OFFSET
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0,9
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COMMENTS
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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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LINKS
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FORMULA
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a(n) = 2*a(n-6) + a(n-12).
G.f.: x*(1+x+x^4+x^5-x^6+x^8+x^9)/(1-2*x^6-x^12).
a(6*n) = a(6*n+3) = a(6*n+4) = A000129(n).
a(6*n+2) = a(6*n+5) = A000129(n+1). (End)
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MATHEMATICA
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CoefficientList[Series[x*(1 + x + x^4 + x^5 - x^6 + x^8 + x^9)/(1 - 2 x^6 - x^12), {x, 0, 50}], x] (* G. C. Greubel, Sep 20 2017 *)
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PROG
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(PARI) x='x+O('x^50); Vec(x*(1+x+x^4+x^5-x^6+x^8+x^9)/(1-2*x^6-x^12)) \\ G. C. Greubel, Sep 20 2017
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CROSSREFS
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KEYWORD
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nonn,obsc
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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