A098082 Absolute values of elements of flattened successive matrices B(k), k>=0, read by rows where B(k) = M^k*C where M=[[-1, 1, 0], [0, -1, 1], [1, 1, -1]] and C = [[0, 1, 1], [1, 1, 1], [1, 1, 2]].

0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 1, 0, 3, 4, 3, 4, 3, 4, 3, 1, 3, 7, 7, 7, 7, 4, 7, 4, 0, 10, 14, 11, 14, 11, 4, 11, 4, 3, 24, 25, 15, 25, 15, 1, 15, 1, 10, 49, 40, 16, 40, 16, 9, 16, 9, 24, 89, 56, 7, 56, 7, 33, 7, 33, 49, 145

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 Markov's: (M+I)^n = M^(3*n) (M-1)^n = Sum_{m=0..n} (-1)^m*C(n,m)*M^(n-m).

There seems to be a near matrix ring type behavior of these matrices with I.

Links

Table of n, a(n) for n=0..90.

Mathematica

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

Sequence in context: A033782 A302721 A321740 * A321921 A236419 A114448

Adjacent sequences: A098079 A098080 A098081 * A098083 A098084 A098085

Keyword

nonn,less

Author

Roger L. Bagula, Sep 13 2004

Extensions

Revised by Sean A. Irvine, Feb 09 2026

Status

approved