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).

1, 1, 1, 4, 25, 841, 187489, 1418727556, 2393959458891025, 30567386265691995561839449, 658593751358960570203157512237008273218521, 181183406309644143341701434158730639946454023369335051404405528107396

Offset: 1

Author

Benoit Cloitre, Jul 28 2002

Keywords

• easy
• nonn

Comments

All terms are perfect squares.

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..17

Crossrefs

Cf. A064098, A276095, A276097.

Programs

Mathematica

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 *)

Formula

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

a(n) = A064098(n)^2. - Seiichi Manyama, Aug 18 2016

From Seiichi Manyama, Aug 26 2016: (Start)

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

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