A143763 a(n+1) = (a(n)-n)^2, a(1) = 1.

1, 0, 4, 1, 9, 16, 100, 8649, 74666881, 5575141774264384, 31082205803147712138788845611876, 966103517589229313003894215813508352493573272034098666228778225

Offset: 1

Author

Reinhard Zumkeller, Sep 01 2008

Keywords

• nonn

Comments

Let f(n+1,k) = f(n,k)^2 + k*n*f(n,k) + n^2, f(1, k) = 1:

f(n,0)=A143760(n), f(n,-1)=A143761(n), f(n,+1)=A143762(n),

f(n,-2)=a(n), f(n,+2)=A143764(n), f(n,-3)=A143765(n), f(n,+3)=A143766(n).

Links

• Index entries for sequences of form a(n+1)=a(n)^2 + ... [From _Reinhard Zumkeller_, Sep 11 2008]

Crossrefs

Cf. A000290.

Programs

Mathematica

a=1;Table[a=(n-a)^2,{n,0,16}] (* Vladimir Joseph Stephan Orlovsky, Nov 20 2009 *)
RecurrenceTable[{a[n+1] == (a[n]-n)^2, a[1] == 1}, a, {n, 1, 15}] (* Vaclav Kotesovec, Dec 18 2014 *)
nxt[{n_,a_}]:={n+1,(a-n)^2}; NestList[nxt,{1,1},12][[All,2]] (* Harvey P. Dale, Feb 02 2022 *)

Formula

a(n) ~ c^(2^n), where c = 1.0360416217849060104872070636721393146594472258894124389077919684140867897... . - Vaclav Kotesovec, Dec 18 2014