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A018920 Pisot sequence T(3,10), a(n) = floor(a(n-1)^2/a(n-2)).

%I A018920 #24 Jul 13 2023 09:30:18
%S A018920 3,10,33,108,353,1153,3766,12300,40172,131202,428506,1399501,4570771,
%T A018920 14928140,48755311,159234864,520061125,1698519827,5547366384,
%U A018920 18117700664,59172417076,193257136076,631177877968,2061427183105,6732621943159,21988745758766
%N A018920 Pisot sequence T(3,10), a(n) = floor(a(n-1)^2/a(n-2)).
%H A018920 Colin Barker, <a href="/A018920/b018920.txt">Table of n, a(n) for n = 0..1000</a>
%H A018920 D. W. Boyd, <a href="https://www.researchgate.net/profile/David_Boyd7/publication/262181133_Linear_recurrence_relations_for_some_generalized_Pisot_sequences_-_annotated_with_corrections_and_additions/links/00b7d536d49781037f000000.pdf">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 A018920 <a href="/index/Ph#Pisot">Index entries for Pisot sequences</a>
%F A018920 a(n) = 3*a(n-1) + a(n-2) - a(n-4) - a(n-5) - a(n-6) (holds at least up to n = 1000 but is not known to hold in general).
%p A018920 PisotT := proc(a0,a1,n)
%p A018920     option remember;
%p A018920     if n = 0 then
%p A018920         a0 ;
%p A018920     elif n = 1 then
%p A018920         a1;
%p A018920     else
%p A018920         floor( procname(a0,a1,n-1)^2/procname(a0,a1,n-2)) ;
%p A018920     end if;
%p A018920 end proc:
%p A018920 A018920 := proc(n)
%p A018920     PisotT(3,10,n) ;
%p A018920 end proc: # _R. J. Mathar_, Feb 13 2016
%t A018920 RecurrenceTable[{a[0] == 3, a[1] == 10, a[n] == Floor[a[n - 1]^2/a[n - 2] ]}, a, {n, 0, 30}] (* _Bruno Berselli_, Feb 05 2016 *)
%o A018920 (Magma) Txy:=[3,10]; [n le 2 select Txy[n] else Floor(Self(n-1)^2/Self(n-2)): n in [1..30]]; // _Bruno Berselli_, Feb 05 2016
%o A018920 (PARI) pisotT(nmax, a1, a2) = {
%o A018920   a=vector(nmax); a[1]=a1; a[2]=a2;
%o A018920   for(n=3, nmax, a[n] = floor(a[n-1]^2/a[n-2]));
%o A018920   a
%o A018920 }
%o A018920 pisotT(50, 3, 10) \\ _Colin Barker_, Jul 29 2016
%Y A018920 See A008776 for definitions of Pisot sequences.
%K A018920 nonn
%O A018920 0,1
%A A018920 _R. K. Guy_
%E A018920 Corrected by _David W. Wilson_