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%I #14 Jul 21 2016 08:41:44
%S 3,2,10,20,66,172,502,1388,3938,11036,31110,87452,246162,692460,
%T 1948502,5482060,15424706,43398588,122107174,343560700,966645746,
%U 2719759244,7652334326,21530654892,60578794274,170444884572,479564842182,1349306749532,3796418256466
%N G.f.: (3-4*x-3*x^2)/(1-2*x-3*x^2+2*x^3).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,-2).
%F a(n)=b1^n+b2^n+b3^n where b1, b2, b3 are the roots of x^3-2*x^2-3*x+2.
%F Limit a[n]/a[n-1] as n -> infinity is the largest root.
%t b3 = x /. NSolve[x^3 - 2*x^2 - 3*x + 2 == 0, x][[3]] b2 = x /. NSolve[x^3 - 2*x^2 - 3*x + 2 == 0, x][[2]] b1 = x /. NSolve[x^3 - 2*x^2 - 3*x + 2 == 0, x][[1]] digits = 25 a = Table[2*(b3^n + b1^n + b2^n)/(b3 + b2 + b1), {n, 0, digits}]
%o (PARI) a(n)=if(n<0, 0, polsym(x^3-2*x^2-3*x+2,n)[n+1])
%o (PARI) a(n)=([0,1,0; 0,0,1; -2,3,2]^n*[3;2;10])[1,1] \\ _Charles R Greathouse IV_, Jul 21 2016
%K nonn,easy
%O 0,1
%A _Roger L. Bagula_, May 22 2005
%E Edited by _N. J. A. Sloane_, Jun 08 2007
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