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A020736 Pisot sequence L(5,8).

%I A020736 #16 Sep 08 2022 08:44:45
%S A020736 5,8,13,22,38,66,115,201,352,617,1082,1898,3330,5843,10253,17992,
%T A020736 31573,55406,97230,170626,299427,525457,922112,1618193,2839730,
%U A020736 4983378,8745218,15346787,26931733,47261896,82938845,145547526,255418102,448227522,786584467
%N A020736 Pisot sequence L(5,8).
%H A020736 Colin Barker, <a href="/A020736/b020736.txt">Table of n, a(n) for n = 0..1000</a>
%F A020736 a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - a(n-4) (holds at least up to n = 1000 but is not known to hold in general).
%t A020736 RecurrenceTable[{a[0] == 5, a[1] == 8, a[n] == Ceiling[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 40}] (* _Bruno Berselli_, Feb 05 2016 *)
%o A020736 (Magma) Lxy:=[5,8]; [n le 2 select Lxy[n] else Ceiling(Self(n-1)^2/Self(n-2)): n in [1..40]]; // _Bruno Berselli_, Feb 05 2016
%o A020736 (PARI) pisotL(nmax, a1, a2) = {
%o A020736   a=vector(nmax); a[1]=a1; a[2]=a2;
%o A020736   for(n=3, nmax, a[n] = ceil(a[n-1]^2/a[n-2]));
%o A020736   a
%o A020736 }
%o A020736 pisotL(50, 5, 8) \\ _Colin Barker_, Aug 07 2016
%Y A020736 See A008776 for definitions of Pisot sequences.
%K A020736 nonn
%O A020736 0,1
%A A020736 _David W. Wilson_