A097868 The n-th group (n>=0) of 16 consecutive terms are the entries, read by rows, of the 4 X 4 matrix A[n]=MA[n-1] (n>=1), where M is the 4 X 4 matrix [[0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [1, 0, 0, 1]] and A[0] is the 4 X 4 matrix [[1, 1, 1, 1], [1, 1, 1, 2], [1, 1, 2, 3], [1, 2, 3, 4]].

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 2, 3, 4, 1, 1, 1, 2, 1, 1, 2, 3, 1, 2, 3, 4, 2, 3, 4, 5, 1, 1, 2, 3, 1, 2, 3, 4, 2, 3, 4, 5, 3, 4, 5, 7, 1, 2, 3, 4, 2, 3, 4, 5, 3, 4, 5, 7, 4, 5, 7, 10, 2, 3, 4, 5, 3, 4, 5, 7, 4, 5, 7, 10, 5, 7, 10, 14, 3, 4, 5, 7, 4, 5, 7, 10, 5, 7, 10, 14, 7, 10, 14, 19, 4, 5, 7, 10

Offset

0,8

Links

Table of n, a(n) for n=0..99.

Example

Since MA[0]=[[1,1,1,2],[1,1,2,3],[1,2,3,4],[2,3,4,5]], the 1st group (following the 0th group) of 16 terms is 1,1,1,2,1,1,2,3,1,2,3,4,2,3,4,5.

Maple

with(linalg): M:=matrix(4, 4, [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1]): A[0]:=matrix(4, 4, [1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 2, 3, 4]): for n from 1 to 8 do A[n]:=multiply(M, A[n-1]) od: seq(seq(seq(A[k][i, j], j=1..4), i=1..4), k=0..8);

Mathematica

(* Minimal Pisot theta 1 4 X 4 Markov sequence*) digits=15 M={{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, 1}} A[n_]:=M.A[n-1]; A[0]:={{1, 1, 1, 1}, {1, 1, 1, 2}, {1, 1, 2, 3}, {1, 2, 3, 4}}; i=IdentityMatrix[4] Det[M-x*i] (* flattened sequence of 4 X 4 matrices made with a theta1 Minimal Pisot recurrence*) b=Flatten[Table[M.A[n], {n, 0, digits}]] Dimensions[b][[1]] b=Flatten[Table[M.A[n], {n, 0, digits}]]

Crossrefs

Sequence in context: A079246 A309014 A070990 * A025830 A389613 A083796

Adjacent sequences: A097865 A097866 A097867 * A097869 A097870 A097871

Keyword

nonn

Author

Roger L. Bagula, Aug 31 2004

Extensions

Edited by N. J. A. Sloane, May 20 2006

Status

approved