A000317 a(n+1) = a(n)^2 - a(n) a(n-1) + a(n-1)^2.

1, 2, 3, 7, 37, 1159, 1301767, 1693089917617, 2866551265129451657751739, 8217116155610406522540626640615749228405055996847

Offset

1,2

Links

T. D. Noe, Table of n, a(n) for n = 1..14

Emmanuel Ferrand, Deformations of the Taylor Formula, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.7.

Maple

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;

Mathematica

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 *)
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 *)
nxt[{a_, b_}]:={b, b^2-a *b+a^2}; NestList[nxt, {1, 2}, 10][[All, 1]] (* Harvey P. Dale, Aug 01 2020 *)

Prog

(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

Crossrefs

Sequence in context: A034900 A079388 A183605 * A047024 A182219 A227777

Adjacent sequences: A000314 A000315 A000316 * A000318 A000319 A000320

Keyword

nonn

Author

N. J. A. Sloane

Status

approved