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A097964 Fractional Pisot with constant ration for (1/2,1/2) Bezier. 0
2, 5, 7, 3, 5, 8, 2, 3, 6, 4, 7, 12, 6, 11, 17, 4, 8, 12, 10, 17, 27, 12, 21, 34, 9, 15, 24, 20, 34, 54, 25, 42, 68, 18, 30, 49, 40, 67, 108, 50, 85, 136, 36, 61, 97, 80, 135, 216, 101, 170, 271, 72, 121, 194, 160, 270, 430, 201, 339, 541, 144, 242, 387, 320, 538, 859, 402 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..66.

FORMULA

M=N[4^(1/3)*({{0, 1, 0}, {1, 1, 0}, {0, 0, 0}}/2+{{0, 1, 0}, {0, 0, 1}, {1, 1, 0}}/2)]; A[n_]:=M.A[n-1]; A[0]:={{0, 1, 1}, {1, 1, 2}, {1, 2, 3}};

MATHEMATICA

(* Fractional Pisot 3 X 3 Markov sequence*) Clear[M, A, x] digits=21; M=N[4^(1/3)*({{0, 1, 0}, {1, 1, 0}, {0, 0, 0}}/2+{{0, 1, 0}, {0, 0, 1}, {1, 1, 0}}/2)]; Det[M] A[n_]:=M.A[n-1]; A[0]:={{0, 1, 1}, {1, 1, 2}, {1, 2, 3}}; (* flattened sequence of 3 X 3 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: A093200 A095795 A088531 * A133133 A024710 A140264

Adjacent sequences:  A097961 A097962 A097963 * A097965 A097966 A097967

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Sep 06 2004

STATUS

approved

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Last modified September 30 13:31 EDT 2014. Contains 247425 sequences.