A097865 The n-th 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[n-A[n-1](1,1)] + A[n-A[n-2](1,2)], (M(i,j) denotes the (i,j)-entry of the matrix M).

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

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[2-1]+A[2-1]=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[n-A[n-1][1, 1]]+A[n-A[n-2][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[n-A[n-1][[1, 1]]]+A[n-A[n-2][[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 A328027

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