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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Inspired by the work of Gary Adamson and Jay Kapraff LINKS 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). [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] 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 A025066 A060426 Adjacent sequences:  A097572 A097573 A097574 * A097576 A097577 A097578 KEYWORD nonn AUTHOR Roger L. Bagula, Aug 28 2004 STATUS approved

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