%I A104100
%S A104100 0,20,57,434,1717,10553,47573,265684,1276818,6811097,33775052,176219759,
%T A104100 887333535,4580070573,23235380380,119306276376,607466542861,
%U A104100 3111219668378,15869382126877,81176527531045,414414451168349
%N A104100 First entry of the vector (M^n)v, where M is the 4 x 4 matrix [[0, 1, 
               3, 8], [0, 0, 1, 5], [0, 0, 0, 1], [1, 2, 1, 1]] and v is the column 
               vector [[0, 1, 1, 2].
%C A104100 Characteristic polynomial of the matrix M is x^4-x^3-19x^2-10x-1.
%F A104100 Recurrence relation: a(n)=a(n-1)+19a(n-2)+10a(n-3)+a(n-4) for n>=4; a(0)=0, 
               a(1)=20, a(2)=57, a(3)=434.
%F A104100 O.g.f.: x*(-20-37*x+3*x^2)/(-1+x+19*x^2+10*x^3+x^4). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Dec 05 2007
%p A104100 a[0]:=0:a[1]:=20:a[2]:=57:a[3]:=434: for n from 4 to 22 do a[n]:=a[n-1]+19*a[n-2]+10*a[n-3]+a[n-4] 
               od: seq(a[n],n=0..22);
%t A104100 Ms = {{0, 1, 3, 8}, {0, 0, 1, 5}, {0, 0, 0, 1}, {1, 2, 1, 1}}; z[0] = 
               {0, 1, 1, 2}; z[n_] := z[n] = Ms.z[n - 1] a=Table[z[n][[1]], {n, 
               0, 50}]
%Y A104100 Sequence in context: A109806 A012483 A051872 this_sequence A069132 A124713 
               A126374
%Y A104100 Adjacent sequences: A104097 A104098 A104099 this_sequence A104101 A104102 
               A104103
%K A104100 nonn
%O A104100 0,2
%A A104100 Roger Bagula (rlbagulatftn(AT)yahoo.com), Mar 31 2005
%E A104100 Edited by N. J. A. Sloane (njas(AT)research.att.com), May 20 2006