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%I #27 Sep 08 2022 08:44:45
%S 5,9,16,28,49,85,147,254,438,755,1301,2241,3860,6648,11449,19717,
%T 33955,58474,100698,173411,298629,514265,885608,1525092,2626337,
%U 4522773,7788595,13412614,23097646,39776083,68497749,117958865,203135052,349815584,602411753
%N Pisot sequence T(5,9), a(n) = floor(a(n-1)^2/a(n-2)).
%H Colin Barker, <a href="/A020750/b020750.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = 2*a(n-1) - 2*a(n-4) + a(n-5) (holds at least up to n = 40000 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] == 9, a[n] == Floor[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 40}] (* _Bruno Berselli_, Feb 04 2016 *)
%t nxt[{a_,b_}]:={b,Floor[b^2/a]}; NestList[nxt,{5,9},40][[All,1]] (* _Harvey P. Dale_, Aug 29 2021 *)
%o (Magma) Iv:=[5, 9]; [n le 2 select Iv[n] else Floor(Self(n-1)^2/Self(n-2)): n in [1..40]]; // _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, 5, 9) \\ _Colin Barker_, Jul 29 2016
%Y See A008776 for definitions of Pisot sequences.
%K nonn
%O 0,1
%A _David W. Wilson_
%E Deleted unproved recurrence and program based on it. - _N. J. A. Sloane_, Feb 04 2016
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