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A048587 Pisot sequence L(6,10).

%I A048587 #17 Sep 08 2022 08:44:57
%S A048587 6,10,17,29,50,87,152,266,466,817,1433,2514,4411,7740,13582,23834,
%T A048587 41825,73397,128802,226031,396656,696082,1221538,2143649,3761841,
%U A048587 6601570,11584947,20330164,35676950,62608682,109870577,192809421,338356946,593775047,1042002568
%N A048587 Pisot sequence L(6,10).
%H A048587 Colin Barker, <a href="/A048587/b048587.txt">Table of n, a(n) for n = 0..1000</a>
%F A048587 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 A048587 RecurrenceTable[{a[0] == 6, a[1] == 10, a[n] == Ceiling[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 40}] (* _Bruno Berselli_, Feb 05 2016 *)
%o A048587 (Magma) Lxy:=[6,10]; [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 A048587 (PARI) pisotL(nmax, a1, a2) = {
%o A048587   a=vector(nmax); a[1]=a1; a[2]=a2;
%o A048587   for(n=3, nmax, a[n] = ceil(a[n-1]^2/a[n-2]));
%o A048587   a
%o A048587 }
%o A048587 pisotL(50, 6, 10) \\ _Colin Barker_, Aug 07 2016
%Y A048587 Subsequence of A018908.
%Y A048587 See A008776 for definitions of Pisot sequences.
%K A048587 nonn
%O A048587 0,1
%A A048587 _David W. Wilson_