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Pisot sequence T(2,9), a(n) = floor(a(n-1)^2/a(n-2)).
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%I #18 Sep 08 2022 08:44:45

%S 2,9,40,177,783,3463,15315,67730,299533,1324671,5858296,25908042,

%T 114577112,506711954,2240910072,9910320668,43827932664,193826995709,

%U 857190882207,3790886846546,16765020932461,74142526074589,327891876477017,1450086587978657

%N Pisot sequence T(2,9), a(n) = floor(a(n-1)^2/a(n-2)).

%H Colin Barker, <a href="/A020728/b020728.txt">Table of n, a(n) for n = 0..1000</a>

%F Pisot sequence T(x, y): a(0) = x, a(1) = y, a(n) = floor(a(n-1)^2/a(n-2)).

%t RecurrenceTable[{a[0] == 2, a[1] == 9, a[n] == Floor[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 30}] (* _Bruno Berselli_, Feb 04 2016 *)

%o (PARI) lista(nn) = {print1(x = 2, ", ", y = 9, ", "); for (n=1, nn, z = y^2\x; print1(z, ", "); x = y; y = z;);} \\ _Michel Marcus_, Feb 04 2016

%o (Magma) Iv:=[2,9]; [n le 2 select Iv[n] else Floor(Self(n-1)^2/Self(n-2)): n in [1..30]]; // _Bruno Berselli_, Feb 04 2016

%o (PARI) pisotT(nmax, a1, a2) = {

%o a=vector(nmax); a[1]=a1; a[2]=a2;

%o for(n=3, nmax, a[n] = floor(a[n-1]^2/a[n-2]));

%o a

%o }

%o pisotT(50, 2, 9) \\ _Colin Barker_, Jul 29 2016

%Y See A008776 for definitions of Pisot sequences.

%K nonn

%O 0,1

%A _David W. Wilson_