%I A107377
%S A107377 0,1,1,2,5,19,84,393,1865,8886,42381,202187,964640,4602409,21958729,
%T A107377 104768258,499864605,2384926971,11378834836,54290082897,259025915025,
%U A107377 1235850473974,5896423120549,28132695944723,134225201438720
%N A107377 Sequence produced by 4 X 4 Markov chain with symmetric quartic characteristic 
               polynomial x^4-5*x^3+5*x+1.
%C A107377 Setting m=3 gives a Fibonacci sequence.
%F A107377 Let m=5, M={{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {-1, -m, 0, m}}, 
               v[n]=M.v[n-1], then a(n) = v[n][[1]].
%t A107377 m = 5 M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {-1, -m, 0, m}} 
               Expand[Det[M - x*IdentityMatrix[4]]] NSolve[Det[M - x*IdentityMatrix[4]] 
               == 0, x] v[1] = {0, 1, 1, 2}; v[n_] := v[n] = M.v[n - 1]; digits 
               = 50; a = Table[v[n][[1]], {n, 1, digits}]
%Y A107377 Cf. A107378.
%Y A107377 Sequence in context: A150027 A058131 A138911 this_sequence A058132 A002851 
               A124348
%Y A107377 Adjacent sequences: A107374 A107375 A107376 this_sequence A107378 A107379 
               A107380
%K A107377 nonn
%O A107377 0,4
%A A107377 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 24 2005
%E A107377 Edited by N. J. A. Sloane (njas(AT)research.att.com), Jul 13 2007