Search: id:A106732
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%I A106732
%S A106732 0,3,15,66,285,1227,5280,22719,97755,420618,1809825,7787271,33506880,
%T A106732 144172587,620342295,2669193714,11484941685,49417127283,212630811360,
%U A106732 914902674951,3936620940675,16938396678522,72882120570585
%V A106732 0,-3,-15,-66,-285,-1227,-5280,-22719,-97755,-420618,-1809825,-7787271,
               -33506880,
%W A106732 -144172587,-620342295,-2669193714,-11484941685,-49417127283,-212630811360,
%X A106732 -914902674951,-3936620940675,-16938396678522,-72882120570585
%N A106732 First entry of the vector (M^n)v, where M is the 2 X 2 matrix [[0,-3],
               [1,5]] and v is the column vector [0,1].
%C A106732 Real Pisot roots (the eigenvalues of M): (5-sqrt(13))/2=0.697224,(5+sqrt(13))/
               2= 4.30278
%F A106732 a(n)=first entry of v[n], where v[n]=Mv[n-1], M is the 2 X 2 matrix [[0, 
               -3], [1, 5]] and v[0] is the column vector [0,1]. G.f.=-3x/(1-5x+3x^2). 
               a(n)=5a(n-1)-3a(n-2); a(0)=0, a(1)=-3.
%F A106732 a(n)=(3/13)*[5/2-(1/2)*sqrt(13)]^n*sqrt(13)-(3/13)*sqrt(13)*[5/2+(1/2)*sqrt(13)]^n, 
               with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Oct 07 2008]
%p A106732 a[0]:=0: a[1]:=-3: for n from 2 to 22 do a[n]:=5*a[n-1]-3*a[n-2] od: 
               seq(a[n],n=0..22);
%t A106732 M = {{0, -3}, {1, 5}} v[1] = {0, 1} v[n_] := v[n] = M.v[n - 1] a = Table[Abs[v[n][[1]]], 
               {n, 1, 50}]
%Y A106732 Sequence in context: A098102 A144067 A001447 this_sequence A052981 A086200 
               A122558
%Y A106732 Adjacent sequences: A106729 A106730 A106731 this_sequence A106733 A106734 
               A106735
%K A106732 sign
%O A106732 0,2
%A A106732 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 30 2005
%E A106732 Edited by N. J. A. Sloane (njas(AT)research.att.com), Apr 30 2006

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