%I #10 Dec 15 2016 01:25:52
%S 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,
%T 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,
%U 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
%N 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).
%e 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.
%p 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);
%K nonn
%O 0,6
%A _Roger L. Bagula_, Aug 30 2004
%E Edited by _N. J. A. Sloane_, May 20 2006