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A116559
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Sequentually switched Markov of six 2 X 2 matrices based on the SL[2,2] group of Blyth and Robinson that gives a chaotic vector output.
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0
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0, 1, 1, 2, 2, 5, 5, 3, 8, 11, 11, 30, 30, 19, 49, 68, 68, 185, 185, 117, 302, 419, 419, 1140, 1140, 721, 1861, 2582, 2582, 7025, 7025, 4443, 11468, 15911, 15911, 43290, 43290
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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REFERENCES
| Blyth and Robonson,Essential Student Algebra, V5,Groups,J. W. Arrowsmith, Bristol,1986, page 9
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FORMULA
| 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]]
a(n)=6*a(n-6)+a(n-12). G.f.: x(1+x+2x^2+2x^3+5x^4+5x^5-3x^6+2x^7-x^8-x^9)/(1-6x^6-x^12). a(6n+1)=A005667(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 28 2008]
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MATHEMATICA
| 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
| Sequence in context: A005177 A045537 A161622 * A008280 A195710 A063960
Adjacent sequences: A116556 A116557 A116558 * A116560 A116561 A116562
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KEYWORD
| nonn,uned,obsc
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 17 2006
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