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%I #27 Jul 13 2023 09:51:30
%S 8,65,528,4288,34823,282798,2296605,18650749,151462893,1230031456,
%T 9989096027,81121534697,658788680558,5350028537458,43447627739097,
%U 352838558325161,2865404964997647,23269978350457597,188975694202166613,1534673236964508227
%N Define the generalized Pisot sequence T(a(0),a(1)) by: a(n+2) is the greatest integer such that a(n+2)/a(n+1) < a(n+1)/a(n). This is T(8,65).
%C This coincides with the Pisot T(8,65) sequence as defined in A008776 at least up to n <= 14000. - _R. J. Mathar_, Feb 13 2016
%H Colin Barker, <a href="/A022039/b022039.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Ph#Pisot">Index entries for Pisot sequences</a>
%F Empirical g.f.: -(x^6+x^5+x^4+x^3-x-8) / (x^7+x^6+x^5+x^4-x^2-8*x+1). - _Colin Barker_, Dec 02 2014
%t RecurrenceTable[{a[1] == 8, a[2] == 65, a[n] == Ceiling[a[n-1]^2/a[n-2]] - 1}, a, {n, 30}] (* _Bruno Berselli_, Feb 17 2016 *)
%o (PARI)
%o T(a0, a1, maxn) = a=vector(maxn); a[1]=a0; a[2]=a1; for(n=3, maxn, a[n]=floor(a[n-1]^2/a[n-2])); a
%o T(8, 65, 100) \\ _Colin Barker_, Dec 02 2014
%o (Magma) Tiv:=[8,65]; [n le 2 select Tiv[n] else Ceiling(Self(n-1)^2/Self(n-2))-1: n in [1..30]]; // _Bruno Berselli_, Feb 17 2016
%K nonn
%O 0,1
%A _R. K. Guy_
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