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A048589 Pisot sequence L(7,9).

%I A048589 #14 Sep 08 2022 08:44:57
%S A048589 7,9,12,16,22,31,44,63,91,132,192,280,409,598,875,1281,1876,2748,4026,
%T A048589 5899,8644,12667,18563,27204,39868,58428,85629,125494,183919,269545,
%U A048589 395036,578952,848494,1243527,1822476,2670967,3914491,5736964,8407928,12322416,18059377
%N A048589 Pisot sequence L(7,9).
%H A048589 Colin Barker, <a href="/A048589/b048589.txt">Table of n, a(n) for n = 0..1000</a>
%F A048589 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).
%t A048589 RecurrenceTable[{a[0] == 7, a[1] == 9, a[n] == Ceiling[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 50}] (* _Bruno Berselli_, Feb 05 2016 *)
%o A048589 (Magma) Lxy:=[7,9]; [n le 2 select Lxy[n] else Ceiling(Self(n-1)^2/Self(n-2)): n in [1..50]]; // _Bruno Berselli_, Feb 05 2016
%o A048589 (PARI) pisotL(nmax, a1, a2) = {
%o A048589   a=vector(nmax); a[1]=a1; a[2]=a2;
%o A048589   for(n=3, nmax, a[n] = ceil(a[n-1]^2/a[n-2]));
%o A048589   a
%o A048589 }
%o A048589 pisotL(50, 7, 9) \\ _Colin Barker_, Aug 07 2016
%Y A048589 Subsequence of A048585.
%Y A048589 See A008776 for definitions of Pisot sequences.
%K A048589 nonn
%O A048589 0,1
%A A048589 _David W. Wilson_