

A097864


The nth group (n>=0) of 9 consecutive terms are the entries, read by rows, of the 3 X 3 matrix A[n]=MA[n1], where M is the 3 X 3 matrix [[0,1,0],[0,1,0],[1,1,1]] and A[0] is the 3 X 3 matrix [[0,1,1],[1,1,2],[1,2,4]].


0



0, 1, 1, 1, 1, 2, 1, 2, 4, 1, 1, 2, 1, 1, 2, 2, 4, 7, 1, 1, 2, 1, 1, 2, 4, 6, 11, 1, 1, 2, 1, 1, 2, 6, 8, 15, 1, 1, 2, 1, 1, 2, 8, 10, 19, 1, 1, 2, 1, 1, 2, 10, 12, 23, 1, 1, 2, 1, 1, 2, 12, 14, 27, 1, 1, 2, 1, 1, 2, 14, 16, 31, 1, 1, 2, 1, 1, 2, 16, 18, 35, 1, 1, 2, 1, 1, 2, 18, 20, 39, 1, 1, 2, 1, 1, 2
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OFFSET

0,6


LINKS

Table of n, a(n) for n=0..95.


FORMULA

a(n) = 2*a(n9)  a(n18). [R. J. Mathar, Oct 31 2008]


EXAMPLE

Since MA[0]=[[1,1,2],[1,1,2],[2,4,7]), the 1st group (following the 0th group) of 9 terms are 1,1,2,1,1,2,2,4,7.


MAPLE

with(linalg): M:=matrix(3, 3, [0, 1, 0, 0, 1, 0, 1, 1, 1]): A[0]:=matrix(3, 3, [0, 1, 1, 1, 1, 2, 1, 2, 4]): for n from 1 to 11 do A[n]:=multiply(M, A[n1]) od: seq(seq(seq(A[k][i, j], j=1..3), i=1..3), k=0..11);


MATHEMATICA

(* Fibonacci 3 X 3 Markov sequence*) digits=50 M={{0, 1, 0}, {0, 1, 0}, {1, 1, 1}} A[n_]:=M.A[n1]; A[0]:={{0, 1, 1}, {1, 1, 2}, {1, 2, 4}}; (* flattened sequence of 3 X 3 matrices made with a Fibonacci recurrence*) b=Flatten[Table[M.A[n], {n, 0, digits}]] ListPlot[b, PlotJoined>True]


CROSSREFS

Sequence in context: A143446 A110330 A132014 * A097866 A097865 A105245
Adjacent sequences: A097861 A097862 A097863 * A097865 A097866 A097867


KEYWORD

nonn


AUTHOR

Roger L. Bagula, Aug 30 2004


EXTENSIONS

Edited by N. J. A. Sloane, May 13 2006


STATUS

approved



