A097866 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]], A[2]=[[1, 1, 2], [1, 1, 2], [4, 6, 11]] and A[n]=A[abs(n-A[n-1](1, 1))] + A[abs(n-A[n-2](1, 2))] + A[abs(n-A[n-3](1, 3))], (M(i, j) denoting 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, 1, 1, 2, 1, 1, 2, 4, 6, 11, 3, 3, 6, 3, 3, 6, 12, 18, 33, 5, 5, 10, 5, 5, 10, 18, 28, 51, 4, 5, 9, 5, 5, 10, 17, 26, 48, 2, 3, 5, 3, 3, 6, 7, 12, 22, 8, 9, 17, 9, 9, 18, 33, 50, 92, 5, 7, 12, 7, 7, 14, 20, 32, 59, 10, 11, 21, 11, 11, 22, 37, 58

Offset

0,6

Links

Table of n, a(n) for n=0..88.

Example

We have A[2](1,1)=1, A[1](1,2)=1, A[0](1,3)=1 and so A[3] = A[3-1] + A[3-1] + A[3-1] = 3A[2], a matrix with entries (3,3,6,3,3,6,12,18,33), yielding the 28th, 29th, ..., 36th 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);

Crossrefs

Sequence in context: A110330 A132014 A097864 * A097865 A105245 A105246

Adjacent sequences: A097863 A097864 A097865 * A097867 A097868 A097869

Keyword

nonn

Author

Roger L. Bagula, Aug 30 2004

Extensions

Edited by N. J. A. Sloane, May 20 2006

Status

approved