A086851 - OEIS

%I #19 Oct 18 2020 17:10:14

%S 1,1,0,-2,1,-3,4,10,93,8641,74666872,5575141774264374,

%T 31082205803147712138788845611865,

%U 966103517589229313003894215813508352493573272034098666228778213

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

%H Indranil Ghosh, <a href="/A086851/b086851.txt">Table of n, a(n) for n = 0..16</a>

%H <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>

%F a(n) ~ c^(2^n), where c = 1.0178612979109216580505412401816630473815821687019037486630926162018899277... . - _Vaclav Kotesovec_, Dec 18 2014

%p 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:

%t a=1; lst={}; Do[a=a^2-n; AppendTo[lst, a], {n, 0, 14}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Dec 17 2008 *)

%t RecurrenceTable[{a[0] == 1, a[n+1] == a[n]^2 - n}, a, {n, 0, 15}] (* _Vaclav Kotesovec_, Dec 18 2014 *)

%t nxt[{n_,a_}]:={n+1,a^2-n-1}; NestList[nxt,{-1,1},14][[All,2]] (* _Harvey P. Dale_, Oct 18 2020 *)

%Y Cf. A153059, A153059.

%K sign,easy

%O 0,4

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