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A097864
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Matrix recurrence A[n] = M * A[n-1] with A[0] = [[0,1,1],[1,1,2],[1,2,4]] and M = [[0,1,0],[0,1,0],[1,1,1]], flattened.
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0
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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, 1, 1, 2, 1, 1, 2, 6, 8, 15, 1, 1, 2, 1, 1, 2, 8, 10, 19, 1, 1, 2, 1, 1, 2, 10, 12, 23, 1, 1, 2, 1, 1, 2, 12, 14, 27, 1, 1, 2, 1, 1, 2, 14, 16, 31, 1, 1, 2, 1, 1, 2, 16, 18, 35, 1, 1, 2, 1, 1, 2, 18, 20, 39, 1, 1, 2, 1, 1, 2
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OFFSET
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0,6
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COMMENTS
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Previous name was: 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],[0,1,0],[1,1,1]] and A[0] is the 3 X 3 matrix [[0,1,1],[1,1,2],[1,2,4]].
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,-1).
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FORMULA
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a(n) = 2*a(n-9) - a(n-18) for n >= 27. - R. J. Mathar, Oct 31 2008
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MAPLE
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with(linalg):
nmax:=50: M:=matrix(3, 3, [0, 1, 0, 0, 1, 0, 1, 1, 1]): A[0]:=matrix(3, 3, [0, 1, 1, 1, 1, 2, 1, 2, 4]): for n from 1 to nmax do A[n]:=multiply(M, A[n-1]) od:
seq(seq(seq(A[k][i, j], j=1..3), i=1..3), k=0..nmax);
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MATHEMATICA
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LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {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}, 96] (* Georg Fischer, Jan 17 2021 *)
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CROSSREFS
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KEYWORD
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nonn,easy,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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