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%I #13 Aug 09 2015 01:40:34
%S 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,
%T 34,34,55,34,55,55,89,55,89,89,144,89,144,144,233,144,233,233,377,233,
%U 377,377,610,377,610,610,987,610,987,987,1597,987,1597,1597,2584,1597,2584
%N A 2 X 2 matrix Fibonacci sequence.
%C Inspired by the work of _Gary W. Adamson_ and Jay Kapraff.
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 1, 0, 0, 0, 1).
%F M={{0, 1}, {1, 1}} A[n_]:=M.A[n-1]; A[0]:={{0, 1}, {1, 1}};
%F a(n)=a(n-4)+a(n-8). - _R. J. Mathar_, Oct 31 2008
%F 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
%t (* 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}]]
%Y Cf. A000045.
%K nonn
%O 0,4
%A _Roger L. Bagula_, Aug 28 2004
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