A276097 -id:A276097 - cp's OEIS frontend

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

Benoit Cloitre, Jul 28 2002

All terms are perfect squares.

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

Cf. A064098, A276095, A276097.

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 *)

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)

A276257 a(1) = a(2) = a(3) = a(4) = 1; for n>4, a(n) = ( a(n-1)+a(n-2)+a(n-3)+1 )^2 / a(n-4).

Original entry on oeis.org

1, 1, 1, 1, 16, 361, 143641, 20741472361, 26888415586959536281, 2002733778095476250641191709976062096, 27923382501685315585533445603599269911720565853675615809277429923281

Offset: 1

Seiichi Manyama, Aug 25 2016

nonn

All terms are perfect squares.

The next term (a(12)) has 125 digits. - Harvey P. Dale, Jul 04 2019

Seiichi Manyama, Table of n, a(n) for n = 1..15

Cf. A276097, A276256, A276259.

RecurrenceTable[{a[1]==a[2]==a[3]==a[4]==1,a[n]==(a[n-1]+a[n-2]+ a[n-3]+ 1)^2/a[n-4]},a,{n,11}] (* Harvey P. Dale, Jul 04 2019 *)

a(n) = A276259(n)^2
a(n) = 25*a(n-1)*a(n-2)*a(n-3) - 2*a(n-1) - 2*a(n-2) - 2*a(n-3) - 2 - a(n-4).
a(n)*a(n-1)*a(n-2)*a(n-3) = ((a(n) + a(n-1) + a(n-2) + a(n-3) + 1)/5)^2.

cp's OEIS Frontend

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).

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