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A097886 Flattened 5 x 5 matrices: the n-th power a matrix M multiplied by some matrix A. 2
1, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2, 3, 5, 1, 2, 3, 5, 7, 2, 3, 5, 7, 10, 1, 1, 1, 2, 3, 1, 1, 2, 3, 5, 1, 2, 3, 5, 7, 2, 3, 5, 7, 10, 3, 5, 7, 10, 14, 1, 1, 2, 3, 5, 1, 2, 3, 5, 7, 2, 3, 5, 7, 10, 3, 5, 7, 10, 14, 5, 7, 10, 14, 20, 1, 2, 3, 5, 7, 2, 3, 5, 7, 10, 3, 5, 7, 10, 14, 5, 7, 10, 14, 20, 7, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Define the 5 x 5 matrix M=(0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 1, 0, -1, 1, 1) and the 5 x 5 matrix

A = (1, 1, 1, 1, 1; 1, 1, 1, 1, 2; 1, 1, 1, 2, 3; 1, 1, 2, 3, 5; 1, 2, 3, 5, 7).

The n-th block of 25 terms of the sequence is defined by the 25 elements of the matrix product M^n*A.

Apparently the top-left elements of M^n*A, each 25th element of the sequence, are given by |A107332(n+5)|, and all the other elements of the product M^n*A are given by shifting this index in A107332.

So this sequence is an interlacing of 25 copies of the absolute values of A107332. [Edited Nov 17 2009]

LINKS

Table of n, a(n) for n=1..97.

MATHEMATICA

Clear[M, A, x] (* near Minimal Pisot ( near theta2) 5 X 5 Markov sequence*) digits=12 M={{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}, {1, 0, -1, 1, 1}} Det[M] A[n_]:=M.A[n-1]; A[0]:={{1, 1, 1, 1, 1}, {1, 1, 1, 1, 2}, {1, 1, 1, 2, 3}, {1, 1, 2, 3, 5}, {1, 2, 3, 5, 7}}; i=IdentityMatrix[5] Det[M-x*i] (* flattened sequence of 5 X 5 matrices made with a (near theta2) Minimal Pisot recurrence*) b=Flatten[Table[M.A[n], {n, 0, digits}]] Dimensions[b][[1]] ListPlot[b, PlotJoined->True]

CROSSREFS

Sequence in context: A241898 A191090 A319193 * A249298 A088863 A053283

Adjacent sequences:  A097883 A097884 A097885 * A097887 A097888 A097889

KEYWORD

nonn,easy

AUTHOR

Roger L. Bagula, Sep 02 2004

EXTENSIONS

Edited by the Associate Editors of the OEIS, Nov 17 2009

STATUS

approved

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Last modified April 26 04:37 EDT 2019. Contains 322469 sequences. (Running on oeis4.)