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%I #6 Oct 26 2024 03:55:54
%S 4,9,13,23,5,9,15,24,5,8,13,21,1,2,4,6,12,20,32,53,13,23,37,60,12,21,
%T 33,54,3,6,9,15,29,49,79,129,33,57,91,149,30,50,80,130,8,14,22,37,72,
%U 124,196,321,82,138,221,360,72,123,196,319,20,34,55,89,178,298,476,774,201
%N Fractional Pisot 4 X 4 Markov sequence Bezier {1/4,1/2,1/4} of golden mean, theta0 and theta1.
%t digits=Floor[21*3/4];
%t a=Sqrt[2]*2/3^(1/4);
%t M=N[a*({{0, 1, 0, 0}, {1, 1, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}/4+{{0, 1, 0, 0}, {0, 0, 1, 0}, {1, 1, 0, 0}, {0, 0, 0, 0}}/2+{{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, 1}}/4)];
%t Det[M]
%t A[n_]:=M.A[n-1]; A[0]:={{0, 1, 1, 2}, {1, 1, 2, 3}, {1, 2, 3, 5}, {2, 3, 5, 8}};
%t b=Flatten[Table[M.A[n], {n, 1, digits}]]
%t Floor[Abs[b]]
%t Dimensions[b][[1]]
%t ListPlot[b, PlotJoined->True]
%K nonn,uned,obsc
%O 0,1
%A _Roger L. Bagula_, Sep 08 2004