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A097575
A 2 X 2 matrix Fibonacci sequence.
0
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.
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
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Aug 28 2004
STATUS
approved