A143763 - OEIS

A143763

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

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

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OFFSET

1,3

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

Table of n, a(n) for n=1..12.

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

FORMULA

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

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 *)

CROSSREFS

Cf. A000290.

Sequence in context: A244761 A075150 A001254 * A278350 A128626 A193963

Adjacent sequences: A143760 A143761 A143762 * A143764 A143765 A143766

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Sep 01 2008

STATUS

approved