%I A106731
%S A106731 0,2,8,28,96,328,1120,3824,13056,44576,152192,519616,1774080,6057088,
%T A106731 20680192,70606592,241065984,823050752,2810071040,9594182656,32756588544,
%U A106731 111837988864,381838778368,1303679135744,4451038986240,15196797673472
%V A106731 0,-2,-8,-28,-96,-328,-1120,-3824,-13056,-44576,-152192,-519616,-1774080,
               -6057088,
%W A106731 -20680192,-70606592,-241065984,-823050752,-2810071040,-9594182656,-32756588544,
%X A106731 -111837988864,-381838778368,-1303679135744,-4451038986240,-15196797673472
%N A106731 First entry of the vector (M^n)v, where M is the 2 X 2 matrix [[0,-2],
               [1,4]] and v is the column vector [0,1].
%C A106731 Real Pisot roots (the eigenvalues of M): 2-sqrt(2)= 0.585786, 2+sqrt(2)=3.41421. 
               a(n)=-2*A007070(n-1) for n>=1.
%F A106731 a(n)=first entry of v[n], where v[n]=Mv[n-1], M is the 2 X 2 matrix [[0, 
               -2], [1, 4]] and v[0] is the column vector [0,1]. G.f.=-2x/(1-4x+2x^2). 
               a(n)=4a(n-1)-2a(n-2); a(0)=0, a(1)=-2.
%F A106731 a(n)=-(1/2)*sqrt(2)*[2+sqrt(2)]^n+(1/2)*[2-sqrt(2)]^n*sqrt(2), with n>
               =0 [From Paolo P. Lava (ppl(AT)spl.at), Oct 07 2008]
%p A106731 a[0]:=0: a[1]:=-2: for n from 2 to 27 do a[n]:=4*a[n-1]-2*a[n-2] od: 
               seq(a[n],n=0..27);
%t A106731 M = {{0, -2}, {1, 4}} v[1] = {0, 1} v[n_] := v[n] = M.v[n - 1] a = Table[Abs[v[n][[1]]], 
               {n, 1, 50}]
%Y A106731 Cf. A060995, A007070.
%Y A106731 Sequence in context: A087431 A090426 A060995 this_sequence A066796 A104934 
               A056711
%Y A106731 Adjacent sequences: A106728 A106729 A106730 this_sequence A106732 A106733 
               A106734
%K A106731 sign
%O A106731 0,2
%A A106731 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 30 2005
%E A106731 Edited by N. J. A. Sloane (njas(AT)research.att.com), Apr 30 2006