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A048590 Pisot sequence L(8,9).

%I A048590 #21 Sep 08 2022 08:44:57
%S A048590 8,9,11,14,18,24,32,43,58,79,108,148,203,279,384,529,729,1005,1386,
%T A048590 1912,2638,3640,5023,6932,9567,13204,18224,25153,34717,47918,66139,
%U A048590 91289,126003,173918,240054,331340,457340,631255,871306,1202643,1659980,2291232,3162535
%N A048590 Pisot sequence L(8,9).
%H A048590 Colin Barker, <a href="/A048590/b048590.txt">Table of n, a(n) for n = 0..1000</a>
%F A048590 a(n) = 2*a(n-1) - a(n-2) + a(n-4) - a(n-5) for n > 5 (holds at least up to n = 1000 but is not known to hold in general).
%t A048590 RecurrenceTable[{a[0] == 8, a[1] == 9, a[n] == Ceiling[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 50}] (* _Bruno Berselli_, Feb 05 2016 *)
%o A048590 (Magma) Lxy:=[8,9]; [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 A048590 (PARI) pisotL(nmax, a1, a2) = {
%o A048590   a=vector(nmax); a[1]=a1; a[2]=a2;
%o A048590   for(n=3, nmax, a[n] = ceil(a[n-1]^2/a[n-2]));
%o A048590   a
%o A048590 }
%o A048590 pisotL(50, 8, 9) \\ _Colin Barker_, Aug 07 2016
%Y A048590 See A008776 for definitions of Pisot sequences.
%Y A048590 Cf. A003411.
%K A048590 nonn
%O A048590 0,1
%A A048590 _David W. Wilson_