A098004 Fractional Pisot 4 X 4 Markov sequence Bezier {1/4,1/2,1/4} of golden mean, theta0 and theta1.

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, 33, 54, 3, 6, 9, 15, 29, 49, 79, 129, 33, 57, 91, 149, 30, 50, 80, 130, 8, 14, 22, 37, 72, 124, 196, 321, 82, 138, 221, 360, 72, 123, 196, 319, 20, 34, 55, 89, 178, 298, 476, 774, 201

Offset

0,1

Links

Table of n, a(n) for n=0..68.

Formula

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)]; A[n_]:=M.A[n-1]; A[0]:={{0, 1, 1, 2}, {1, 1, 2, 3}, {1, 2, 3, 5}, {2, 3, 5, 8}};

Mathematica

(* Fractional Pisot 4 X 4 Markov sequence Bezier {1/2, 1/2}*) Clear[M, A, x] digits=Floor[21*3/4]; a=Sqrt[2]*2/3^(1/4); 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)]; Det[M] A[n_]:=M.A[n-1]; A[0]:={{0, 1, 1, 2}, {1, 1, 2, 3}, {1, 2, 3, 5}, {2, 3, 5, 8}}; (* flattened sequence of 4 X 4 matrices made with a Fractional Pisot recurrence*) b=Flatten[Table[M.A[n], {n, 1, digits}]] Floor[Abs[b]] Dimensions[b][[1]] ListPlot[b, PlotJoined->True]

Crossrefs

Sequence in context: A022130 A042125 A041905 * A257337 A056227 A048261

Adjacent sequences: A098001 A098002 A098003 * A098005 A098006 A098007

Keyword

nonn

Author

Roger L. Bagula, Sep 08 2004

Status

approved