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A097867
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]].
0
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, 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, 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
OFFSET
0,6
EXAMPLE
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.
MAPLE
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);
CROSSREFS
Sequence in context: A109494 A074292 A156257 * A075344 A144083 A332292
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Aug 31 2004
EXTENSIONS
Edited by N. J. A. Sloane, May 20 2006
STATUS
approved