

A097886


Flattened 5 x 5 matrices: the nth 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
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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 nth block of 25 terms of the sequence is defined by the 25 elements of the matrix product M^n*A.
Apparently the topleft 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[n1]; 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[Mx*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: A191090 A331958 A319193 * A308293 A249298 A088863
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



