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A048580 Pisot sequence L(3,10).

%I A048580 #19 Sep 08 2022 08:44:57
%S A048580 3,10,34,116,396,1352,4616,15760,53808,183712,627232,2141504,7311552,
%T A048580 24963200,85229696,290992384,993510144,3392055808,11581202944,
%U A048580 39540700160,135000394752,460920178688,1573679925248,5372879343616,18344157523968,62630871408640
%N A048580 Pisot sequence L(3,10).
%H A048580 Colin Barker, <a href="/A048580/b048580.txt">Table of n, a(n) for n = 0..1000</a>
%F A048580 a(n) = 4*a(n-1) - 2*a(n-2) (holds at least up to n = 1000 but is not known to hold in general).
%F A048580 Empirical g.f.: (3-2*x)/(1-4*x+2*x^2). [_Colin Barker_, Feb 21 2012]
%t A048580 RecurrenceTable[{a[0] == 3, a[1] == 10, a[n] == Ceiling[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 30}] (* _Bruno Berselli_, Feb 05 2016 *)
%o A048580 (Magma) Lxy:=[3,10]; [n le 2 select Lxy[n] else Ceiling(Self(n-1)^2/Self(n-2)): n in [1..30]]; // _Bruno Berselli_, Feb 05 2016
%o A048580 (PARI) pisotL(nmax, a1, a2) = {
%o A048580   a=vector(nmax); a[1]=a1; a[2]=a2;
%o A048580   for(n=3, nmax, a[n] = ceil(a[n-1]^2/a[n-2]));
%o A048580   a
%o A048580 }
%o A048580 pisotL(50, 3, 10) \\ _Colin Barker_, Aug 07 2016
%Y A048580 It appears that this is a subsequence of A007052.
%Y A048580 See A008776 for definitions of Pisot sequences.
%K A048580 nonn
%O A048580 0,1
%A A048580 _David W. Wilson_