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%I #20 Sep 08 2022 08:44:45
%S 5,8,12,18,27,40,59,87,128,188,276,405,594,871,1277,1872,2744,4022,
%T 5895,8640,12663,18559,27200,39864,58424,85625,125490,183915,269541,
%U 395032,578948,848490,1243523,1822472,2670963,3914487,5736960,8407924,12322412,18059373
%N Pisot sequence T(5,8), a(n) = floor(a(n-1)^2/a(n-2)).
%H Colin Barker, <a href="/A020749/b020749.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4) (holds at least up to n = 1000 but is not known to hold in general).
%F Note the warning in A010925 from Pab Ter (pabrlos(AT)yahoo.com), May 23 2004: [A010925] and other examples show that it is essential to reject conjectured generating functions for Pisot sequences until a proof or reference is provided. - _N. J. A. Sloane_, Jul 26 2016
%t RecurrenceTable[{a[0] == 5, a[1] == 8, a[n] == Floor[a[n - 1]^2/a[n - 2] ]}, a, {n, 0, 40}] (* _Bruno Berselli_, Feb 05 2016 *)
%o (Magma) Txy:=[5,8]; [n le 2 select Txy[n] else Floor(Self(n-1)^2/Self(n-2)): n in [1..40]]; // _Bruno Berselli_, Feb 05 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, 5, 8) \\ _Colin Barker_, Jul 29 2016
%Y Subsequence of A020745.
%Y See A008776 for definitions of Pisot sequences.
%K nonn
%O 0,1
%A _David W. Wilson_
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