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A072882 A nonlinear recurrence of order 3: a(1)=a(2)=a(3)=1; a(n)=(a(n-1)+a(n-2))^2/a(n-3).

%I A072882 #31 Aug 26 2016 09:48:37
%S A072882 1,1,1,4,25,841,187489,1418727556,2393959458891025,
%T A072882 30567386265691995561839449,
%U A072882 658593751358960570203157512237008273218521,181183406309644143341701434158730639946454023369335051404405528107396
%N A072882 A nonlinear recurrence of order 3: a(1)=a(2)=a(3)=1; a(n)=(a(n-1)+a(n-2))^2/a(n-3).
%C A072882 All terms are perfect squares.
%H A072882 Seiichi Manyama, <a href="/A072882/b072882.txt">Table of n, a(n) for n = 1..17</a>
%F A072882 a(n) ~ 1/9 * c^(((1+sqrt(5))/2)^n), where c = 1.6403763522562240514693138664331346215549... . - _Vaclav Kotesovec_, May 06 2015
%F A072882 a(n) = A064098(n)^2. - _Seiichi Manyama_, Aug 18 2016
%F A072882 From _Seiichi Manyama_, Aug 26 2016: (Start)
%F A072882 a(n) = 9*a(n-1)*a(n-2) - 2*a(n-1) - 2*a(n-2) - a(n-3).
%F A072882 a(n)*a(n-1)*a(n-2) = ((a(n) + a(n-1) + a(n-2))/3)^2. (End)
%t A072882 RecurrenceTable[{a[1]==1,a[2]==1,a[3]==1, a[n]==(a[n-1]+a[n-2])^2/a[n-3]},a,{n,1,10}] (* _Vaclav Kotesovec_, May 06 2015 *)
%Y A072882 Cf. A064098, A276095, A276097.
%K A072882 easy,nonn
%O A072882 1,4
%A A072882 _Benoit Cloitre_, Jul 28 2002