%I A107389
%S A107389 0,1,1,2,5,31,144,697,3335,15986,76589,366967,1758240,8424241,40362959,
               193390562,926589845,4439558671,21271203504,101916458857,488311090775,
               2339638995026,11209883884349,53709780426727,
%T A107389 257339018249280,1232985310819681,5907587535849119,28304952368425922,135617174306280485,
               649780919162976511,3113287421508602064,14916656188380033817,71469993520391567015,
               342433311413577801266,1640696563547497439309,
%U A107389 7861049506323909395287,37664550968072049537120,180461705334036338290321,
               864643975702109641914479,4142758173176511871282082,19849146890180449714495925,
               95102976277725736701197551,455665734498448233791491824,2183225696214515432256261577,
               10460462746574128927489816055,50119088036656129205192818706,240134977436706517098474277469,
               1150555799146876456287178568647,5512644018297675764337418565760,26412664292341502365399914260161
%N A107389 A quartic Fibonacci type alternating / chaotic vector Markov sequence 
               of a quartic characteristic: x^4+5*x^2-5*x-1:for m=5.
%F A107389 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] a(n) =Abs[v[n][[1]]]
%F A107389 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]; a(n) =Abs[v[n][[1]]]
%t A107389 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]]] (*-1 - 5 x + 5 x^3 + x^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; aa = Table[Abs[v[n][[1]], {n, 1, digits}]
%t A107389 Clear[M, m, v, aa] (*A107389*)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; aa = Table[Abs[v[n][[1]]], 
               {n, 1, digits}]
%Y A107389 Sequence in context: A127298 A000133 A059086 this_sequence A077483 A119242 
               A068145
%Y A107389 Adjacent sequences: A107386 A107387 A107388 this_sequence A107390 A107391 
               A107392
%K A107389 nonn,uned
%O A107389 0,4
%A A107389 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 24 2005, corrected Sep 
               04 2008