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%I #18 Sep 21 2017 04:30:11
%S 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,
%T 29,41,70,29,29,70,70,99,169,70,70,169,169,239,408,169,169,408,408,
%U 577,985,408,408,985,985,1393,2378,985,985,2378,2378
%N Sequentially switched Markov of six 2 X 2 matrices based on the Anharmonic group that gives a chaotic vector output.
%C 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}.
%D Blyth and Robonson, Essential Student Algebra, V5, Groups, J. W. Arrowsmith, Bristol, 1986, page 9.
%D McKean and Moll, Elliptic Curves, Cambridge, New York, 1997, pages 13, 169-171.
%D Andree, Selections from Modern Algebra, Henry Holt and Co, New York, 1958, pages 86, 91.
%H G. C. Greubel, <a href="/A116560/b116560.txt">Table of n, a(n) for n = 0..1000</a>
%F From _R. J. Mathar_, Nov 28 2008: (Start)
%F a(n) = 2*a(n-6) + a(n-12).
%F G.f.: x*(1+x+x^4+x^5-x^6+x^8+x^9)/(1-2*x^6-x^12).
%F a(6*n) = a(6*n+3) = a(6*n+4) = A000129(n).
%F a(6*n+1) = A001333(n).
%F a(6*n+2) = a(6*n+5) = A000129(n+1). (End)
%t 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 *)
%o (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
%K nonn,obsc
%O 0,9
%A _Roger L. Bagula_, Mar 17 2006
%E Terms a(37) onward added by _G. C. Greubel_, Sep 20 2017
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