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A097864 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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
COMMENTS
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]].
LINKS
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).
FORMULA
a(n) = 2*a(n-9) - a(n-18) for n >= 27. - R. J. Mathar, Oct 31 2008
MAPLE
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);
# Georg Fischer, Jan 17 2021
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A143446 A110330 A132014 * A097866 A097865 A105245
KEYWORD
nonn,easy,less
AUTHOR
Roger L. Bagula, Aug 30 2004
EXTENSIONS
Edited by N. J. A. Sloane, May 13 2006
Definition changed by Georg Fischer, Jan 17 2021
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)