A097867 - OEIS

%I #15 Aug 29 2024 21:32:16

%S 0,1,1,1,1,2,1,2,2,1,1,2,1,2,2,1,2,3,1,2,2,1,2,3,2,3,4,1,2,3,2,3,4,2,

%T 4,5,2,3,4,2,4,5,3,5,7,2,4,5,3,5,7,4,7,9,3,5,7,4,7,9,5,9,12,4,7,9,5,9,

%U 12,7,12,16,5,9,12,7,12,16,9,16,21,7,12,16,9,16,21,12,21,28,9,16,21,12,21,28,16,28,37

%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]=M*A[n-1], where M is the 3 X 3 matrix [[0, 1, 0], [0, 0, 1], [1, 1, 0]] and A[0] is the 3 X 3 matrix [[0, 1, 1], [1, 1, 2], [1, 2, 2]].

%e Since M*A[0]=[[1,1,2],[1,2,2],[1,2,3]], the 1st group (following the 0th group) of 9 terms are 1,1,2,1,2,2,1,2,3.

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

%K nonn

%O 0,6

%A _Roger L. Bagula_, Aug 31 2004

%E Edited by _N. J. A. Sloane_, May 20 2006