login
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).
4

%I #31 Aug 26 2016 09:48:37

%S 1,1,1,4,25,841,187489,1418727556,2393959458891025,

%T 30567386265691995561839449,

%U 658593751358960570203157512237008273218521,181183406309644143341701434158730639946454023369335051404405528107396

%N 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 All terms are perfect squares.

%H Seiichi Manyama, <a href="/A072882/b072882.txt">Table of n, a(n) for n = 1..17</a>

%F a(n) ~ 1/9 * c^(((1+sqrt(5))/2)^n), where c = 1.6403763522562240514693138664331346215549... . - _Vaclav Kotesovec_, May 06 2015

%F a(n) = A064098(n)^2. - _Seiichi Manyama_, Aug 18 2016

%F From _Seiichi Manyama_, Aug 26 2016: (Start)

%F a(n) = 9*a(n-1)*a(n-2) - 2*a(n-1) - 2*a(n-2) - a(n-3).

%F a(n)*a(n-1)*a(n-2) = ((a(n) + a(n-1) + a(n-2))/3)^2. (End)

%t 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 Cf. A064098, A276095, A276097.

%K easy,nonn

%O 1,4

%A _Benoit Cloitre_, Jul 28 2002