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A097575
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A 2 X 2 matrix Fibonacci sequence.
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0
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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
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OFFSET
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0,4
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COMMENTS
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Inspired by the work of Gary Adamson and Jay Kapraff
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LINKS
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Table of n, a(n) for n=0..65.
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FORMULA
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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). [From 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). [From R. J. Mathar, Nov 30 2008]
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MATHEMATICA
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(* 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}]]
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CROSSREFS
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Cf. A000045.
Sequence in context: A053277 A078661 A029263 * A103273 A025066 A060426
Adjacent sequences: A097572 A097573 A097574 * A097576 A097577 A097578
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula, Aug 28 2004
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STATUS
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approved
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