

A097865


The nth group (n>=0) of 9 consecutive terms are the entries, read by rows, of the 3 X 3 matrix A[n], where A[0]= [[0,1,1],[1,1,2],[1,2,4]], A[1]=[[1,1,2],[1,1,2],[2,4,7]] and A[n]=A[nA[n1](1,1)] + A[nA[n2](1,2)], (M(i,j) denotes the (i,j)entry of the matrix M).


0



0, 1, 1, 1, 1, 2, 1, 2, 4, 1, 1, 2, 1, 1, 2, 2, 4, 7, 2, 2, 4, 2, 2, 4, 4, 8, 14, 3, 3, 6, 3, 3, 6, 6, 12, 21, 3, 3, 6, 3, 3, 6, 6, 12, 21, 4, 4, 8, 4, 4, 8, 8, 16, 28, 5, 5, 10, 5, 5, 10, 10, 20, 35, 5, 5, 10, 5, 5, 10, 10, 20, 35, 6, 6, 12, 6, 6, 12, 12, 24, 42, 6, 6, 12, 6, 6, 12, 12, 24, 42, 6, 6
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OFFSET

0,6


COMMENTS

A 3 X 3 matrix Hofstadter type sequence.


LINKS

Table of n, a(n) for n=0..91.


EXAMPLE

We have A[1](1,1)=1, A[0](1,2)=1 and so A[2]=A[21]+A[21]=2A[1], a matrix with entries (2,2,4,2,2,4,4,8,14), yielding the 19th,20th,...,27th terms of the sequence.


MAPLE

with(linalg): A[0]:=matrix(3, 3, [0, 1, 1, 1, 1, 2, 1, 2, 4]): A[1]:=matrix(3, 3, [1, 1, 2, 1, 1, 2, 2, 4, 7]): for n from 2 to 10 do A[n]:=evalm(A[nA[n1][1, 1]]+A[nA[n2][1, 2]]) od: seq(seq(seq(A[k][i, j], j=1..3), i=1..3), k=0..10);


MATHEMATICA

Clear[A] (* Hofstadter 3 X 3 Matrix sequence*) digits=50 A[n_]:=A[n]=A[nA[n1][[1, 1]]]+A[nA[n2][[1, 2]]]; A[0]:={{0, 1, 1}, {1, 1, 2}, {1, 2, 4}}; A[1]:={{1, 1, 2}, {1, 1, 2}, {2, 4, 7}}; (* flattened sequence of 3 X 3 matrices made with a Hofstadter recurrence*) b=Flatten[Table[A[n], {n, 0, digits}]] ListPlot[b, PlotJoined>True]


CROSSREFS

Sequence in context: A132014 A097864 A097866 * A105245 A105246 A193829
Adjacent sequences: A097862 A097863 A097864 * A097866 A097867 A097868


KEYWORD

nonn


AUTHOR

Roger L. Bagula, Aug 30 2004


EXTENSIONS

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


STATUS

approved



