A014253 a(n) = b(n)^2, where b(n) = b(n-1)^2 + b(n-2)^2 (A000283).

0, 1, 1, 4, 25, 841, 749956, 563696135209, 317754178344723197077225, 100967717855888389973004528722798800700252204356

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..13
• Index entries for sequences of form a(n+1)=a(n)^2 + ...

Programs

Magma

[0] cat [n le 2 select 1 else (Self(n-1)+Self(n-2))^2: n in [1..10]]; // Vincenzo Librandi, Apr 02 2015

Mathematica

RecurrenceTable[{a[n]==(a[n-1]+a[n-2])^2, a[0]==0, a[1]==1}, a, {n,0,10}] (* G. C. Greubel, Jun 18 2019 *)

PARI

m=10; v=concat([0,1], vector(m-2)); for(n=3, m, v[n]=(v[n-1] + v[n-2])^2); v \\ G. C. Greubel, Jun 18 2019

Sage

def a(n):
    if (n==0): return 0
    elif (n==1): return 1
    else: return (a(n-1) + a(n-2))^2
[a(n) for n in (0..10)] # G. C. Greubel, Jun 18 2019

Formula

a(n+2) = (a(n+1) + a(n))^2. - Benoit Cloitre, Dec 29 2001