A086851 a(0) = 1, a(n+1) = a(n)^2 - n.

1, 1, 0, -2, 1, -3, 4, 10, 93, 8641, 74666872, 5575141774264374, 31082205803147712138788845611865, 966103517589229313003894215813508352493573272034098666228778213

Offset: 0

Author

David McLeod Moulton (dmoulton(AT)asianinc.org), Aug 18 2003

Keywords

• sign
• easy

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..16
• Index entries for sequences of form a(n+1)=a(n)^2 + ...

Crossrefs

Cf. A153059, A153059.

Programs

Maple

a := proc(n) option remember: if n=0 then RETURN(1) fi: a(n-1)^2-n+1: end: for n from 0 to 15 do printf(`%d,`,a(n)) od:

Mathematica

a=1; lst={}; Do[a=a^2-n; AppendTo[lst, a], {n, 0, 14}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 17 2008 *)
RecurrenceTable[{a[0] == 1, a[n+1] == a[n]^2 - n}, a, {n, 0, 15}] (* Vaclav Kotesovec, Dec 18 2014 *)
nxt[{n_,a_}]:={n+1,a^2-n-1}; NestList[nxt,{-1,1},14][[All,2]] (* Harvey P. Dale, Oct 18 2020 *)

Formula

a(n) ~ c^(2^n), where c = 1.0178612979109216580505412401816630473815821687019037486630926162018899277... . - Vaclav Kotesovec, Dec 18 2014