Search: id:A106707
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%I A106707
%S A106707 0,1,4,15,56,209,780,2911,10864,40545,151316,564719,2107560,7865521,
%T A106707 29354524,109552575,408855776,1525870529,5694626340,21252634831,79315912984,
%U A106707 296011017105,1104728155436,4122901604639,15386878263120,57424611447841
%V A106707 0,-1,-4,-15,-56,-209,-780,-2911,-10864,-40545,-151316,-564719,-2107560,
               -7865521,
%W A106707 -29354524,-109552575,-408855776,-1525870529,-5694626340,-21252634831,
               -79315912984,
%X A106707 -296011017105,-1104728155436,-4122901604639,-15386878263120,-57424611447841
%N A106707 First entry of the vector (M^n)v, where M is the 2 X 2 matrix [[0,-1],
               [1,4]] and v is the column vector [0,1].
%C A106707 Real Pisot roots (the eigenvalues of M): 2-sqrt(3)=0.267949, 2+sqrt(3)=3.73205.
%H A106707 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A106707 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A106707 a(n)=first entry of v[n], where v[n]=Mv[n-1], M is the 2 X 2 matrix [[0, 
               -1], [1, 4]] and v[0] is the column vector [0,1]. G.f.=-x/(1-4x+x^2). 
               a(n)=4a(n-1)-a(n-2); a(0)=0, a(1)=-1.
%F A106707 a(n)=(1/6)*sqrt(3)*[2-sqrt(3)]^n-(1/6)*sqrt(3)*[2+sqrt(3)]^n, with n>
               =0 [From Paolo P. Lava (ppl(AT)spl.at), Oct 06 2008]
%p A106707 a[0]:=0: a[1]:=-1: for n from 2 to 27 do a[n]:=4*a[n-1]-a[n-2] od: seq(a[n],
               n=0..27);
%t A106707 M = {{0, -1}, {1, 4}} v[1] = {0, 1} v[n_] := v[n] = M.v[n - 1] a = Table[Abs[v[n][[1]]], 
               {n, 1, 50}]
%Y A106707 Cf. A001076, A001353.
%Y A106707 Sequence in context: A077824 A010905 A001353 this_sequence A125905 A026030 
               A047038
%Y A106707 Adjacent sequences: A106704 A106705 A106706 this_sequence A106708 A106709 
               A106710
%K A106707 sign
%O A106707 0,3
%A A106707 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 30 2005
%E A106707 Edited by N. J. A. Sloane (njas(AT)research.att.com), Apr 30 2006

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