|
%I #33 Sep 08 2022 08:44:27
%S 1,2,3,7,37,1159,1301767,1693089917617,2866551265129451657751739,
%T 8217116155610406522540626640615749228405055996847
%N a(n+1) = a(n)^2 - a(n) a(n-1) + a(n-1)^2.
%H T. D. Noe, <a href="/A000317/b000317.txt">Table of n, a(n) for n = 1..14</a>
%H Emmanuel Ferrand, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL10/Ferrand/ferrand8.html">Deformations of the Taylor Formula</a>, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.7.
%p A000317 := proc(n) option remember; if n <=2 then n else A000317(n-1)^2-A000317(n-1)*A000317(n-2)+A000317(n-2)^2; fi; end;
%t t = {1, 2}; Do[AppendTo[t, t[[-1]]^2 - t[[-1]] t[[-2]] + t[[-2]]^2], {n, 10}]; t (* _T. D. Noe_, Jun 19 2012 *)
%t RecurrenceTable[{a[n] == a[n-1]^2 - a[n-1]*a[n-2] + a[n-2]^2, a[1] == 1, a[2] == 2}, a, {n, 1, 10}] (* _Jean-François Alcover_, Feb 07 2016 *)
%t nxt[{a_,b_}]:={b,b^2-a *b+a^2}; NestList[nxt,{1,2},10][[All,1]] (* _Harvey P. Dale_, Aug 01 2020 *)
%o (Magma) I:=[1,2]; [n le 2 select I[n] else Self(n-1)^2 - Self(n-1)*Self(n-2) + Self(n-2)^2: n in [1..11]]; // _Vincenzo Librandi_, Jul 18 2015
%K nonn
%O 1,2
%A _N. J. A. Sloane_
|
