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, 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

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

Table of n, a(n) for n=0..95.

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

Adjacent sequences: A097861 A097862 A097863 * A097865 A097866 A097867

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