A097575 A 2 X 2 matrix Fibonacci sequence.

1, 1, 1, 2, 1, 2, 2, 3, 2, 3, 3, 5, 3, 5, 5, 8, 5, 8, 8, 13, 8, 13, 13, 21, 13, 21, 21, 34, 21, 34, 34, 55, 34, 55, 55, 89, 55, 89, 89, 144, 89, 144, 144, 233, 144, 233, 233, 377, 233, 377, 377, 610, 377, 610, 610, 987, 610, 987, 987, 1597, 987, 1597, 1597, 2584, 1597, 2584

Offset

0,4

Comments

Inspired by the work of Gary W. Adamson and Jay Kapraff.

Links

Table of n, a(n) for n=0..65.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 1, 0, 0, 0, 1).

Formula

M={{0, 1}, {1, 1}} A[n_]:=M.A[n-1]; A[0]:={{0, 1}, {1, 1}};

a(n)=a(n-4)+a(n-8). - R. J. Mathar, Oct 31 2008

a(n)=a(n-4)+a(n-8). a(4n)=A000045(n+1). a(4n+1)=a(4n+2)=A000045(n+2). a(4n+3)=A000045(n+3). - R. J. Mathar, Nov 30 2008

Mathematica

(* Fibonacci 2 X 2 Markov sequence*) digits=100 M={{0, 1}, {1, 1}} A[n_]:=M.A[n-1]; A[0]:={{0, 1}, {1, 1}}; (* flattened sequence of 2 X 2 matrices made with a Fibonacci recurrence*) b=Flatten[Table[M.A[n], {n, 0, digits}]]

Crossrefs

Cf. A000045.

Sequence in context: A053277 A078661 A029263 * A103273 A289120 A025066

Adjacent sequences: A097572 A097573 A097574 * A097576 A097577 A097578

Keyword

nonn

Author

Roger L. Bagula, Aug 28 2004

Status

approved