cp's OEIS Frontend

A020727 Pisot sequence P(2,7): a(0)=2, a(1)=7, thereafter a(n+1) is the nearest integer to a(n)^2/a(n-1).

%I A020727 #34 Sep 08 2022 08:44:45
%S A020727 2,7,24,82,280,956,3264,11144,38048,129904,443520,1514272,5170048,
%T A020727 17651648,60266496,205762688,702517760,2398545664,8189147136,
%U A020727 27959497216,95459694592,325919783936,1112759746560,3799199418368,12971278180352,44286713884672
%N A020727 Pisot sequence P(2,7): a(0)=2, a(1)=7, thereafter a(n+1) is the nearest integer to a(n)^2/a(n-1).
%C A020727 Also Pisot sequence T(2,7). - _R. K. Guy_
%C A020727 It appears that 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).
%C A020727 The recurrence holds up to n = 10^5. - _Ralf Stephan_, Sep 03 2013
%C A020727 Empirical g.f.: (2-x)/(1-4*x+2*x^2). - _Colin Barker_, Feb 21 2012
%H A020727 Colin Barker, <a href="/A020727/b020727.txt">Table of n, a(n) for n = 0..1000</a>
%t A020727 RecurrenceTable[{a[0] == 2, a[1] == 7, a[n] == Floor[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 30}] (* _Bruno Berselli_, Feb 04 2016 *)
%o A020727 (Magma) Iv:=[2,7]; [n le 2 select Iv[n] else Floor(Self(n-1)^2/Self(n-2)): n in [1..30]]; // _Bruno Berselli_, Feb 04 2016
%o A020727 (PARI) pisotP(nmax, a1, a2) = {
%o A020727   a=vector(nmax); a[1]=a1; a[2]=a2;
%o A020727   for(n=3, nmax, a[n] = ceil(a[n-1]^2/a[n-2]-1/2));
%o A020727   a
%o A020727 }
%o A020727 pisotP(50, 2, 7) \\ _Colin Barker_, Aug 08 2016
%Y A020727 It appears that this is a subsequence of A003480.
%Y A020727 See A008776 for definitions of Pisot sequences.
%K A020727 nonn
%O A020727 0,1
%A A020727 _David W. Wilson_
%E A020727 Edited by _N. J. A. Sloane_, Aug 17 2009 at the suggestion of _R. J. Mathar_.