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%I #22 Jul 13 2023 09:27:30
%S 2,5,12,28,65,150,346,798,1840,4242,9779,22543,51967,119796,276157,
%T 636604,1467515,3382951,7798460,17977197,41441465,95531857,220222323,
%U 507661769,1170274058,2697743762,6218903474,14335965099,33047609788,76182140871,175616894078
%N Pisot sequence T(2,5), a(n) = floor(a(n-1)^2/a(n-2)).
%H Colin Barker, <a href="/A018914/b018914.txt">Table of n, a(n) for n = 0..1000</a>
%H D. W. Boyd, <a href="https://www.researchgate.net/publication/258834801">Linear recurrence relations for some generalized Pisot sequences</a>, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.
%H <a href="/index/Ph#Pisot">Index entries for Pisot sequences</a>
%F a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) - a(n-6) (holds at least up to n = 1000 but is not known to hold in general).
%t RecurrenceTable[{a[0] == 2, a[1] == 5, a[n] == Floor[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 40}] (* _Bruno Berselli_, Feb 04 2016 *)
%o (Magma) Iv:=[2,5]; [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 }
%Y See A008776 for definitions of Pisot sequences.
%K nonn
%O 0,1
%A _R. K. Guy_
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