OFFSET
0,9
COMMENTS
Minimal Pisot generator matrix minus identity 3 X 3 Markov sequence.
The minimal Pisot generator matrix M has identity: M^3-M-I=0 Which suggests the binomial forms as Markovs: (M+I)^n=M^(3*n) (M-1)^n=Sum[(-1)^m*C(n,m)*M^(n-m),{m,0,n}] There seems to be a near Matrix Ring type behavior of these Matrices with I.
MATHEMATICA
(*Minimal Pisot generator matrix minus identity 3 X 3 Markov sequence*) Clear[x, M, A] digits=21 M={{0, 1, 0}, {0, 0, 1}, {1, 1, 0}} M0=M-IdentityMatrix[3] Det[M0] A[n_]:=M0.A[n-1]; A[0]:={{0, 1, 1}, {1, 1, 1}, {1, 1, 2}}; (* flattened sequence of 3 X 3 matrices made with an alternating recurrence*) b=Flatten[Table[Abs[A[n]], {n, 0, digits}]] ListPlot[b, PlotJoined->True]
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Sep 13 2004
STATUS
approved