cp's OEIS Frontend

A259048 u(1) = v(1) = 1, u(n) = u(n-1) + v(n-1), v(n) = u(n-1)^2 + v(n-1)^2, a(n) = u(n).

%I A259048 #24 Sep 08 2022 08:46:13
%S A259048 1,2,4,12,92,6636,42839036,1834614576635532,
%T A259048 3365810487617338033584723922844,
%U A259048 11328680238554850474377984661704304183660014108982249765031212
%N A259048 u(1) = v(1) = 1, u(n) = u(n-1) + v(n-1), v(n) = u(n-1)^2 + v(n-1)^2, a(n) = u(n).
%F A259048 a(n) = a(n-1)^2 + a(n-1) - 2*a(n-1)*a(n-2) + 2*a(n-2)^2, a(1) = 1, a(2) = 2.
%e A259048 u(2) = 2, v(2) = 2; u(3) = 4, v(3) = 8; u(4) = 12, v(4) = 80; u(5) = 92, v(5) = 6544.
%t A259048 RecurrenceTable[{x[n+ 2] == x[n+1]^2 + x[n+1] - 2*x[n+1]*x[n] + 2*x[n]^2, x[1] == 1, x[2] == 2 }, x, {n, 10}]
%o A259048 (Magma) I:=[1,2]; [n le 2 select I[n] else Self(n-1)^2+Self(n-1)-2*Self(n-1)*Self(n-2)+2*Self(n-2)^2: n in [1..11]]; // _Vincenzo Librandi_, Jun 18 2015
%o A259048 (Sage)
%o A259048 def main(size):
%o A259048     u=[1]; v=[1]; a=[1]
%o A259048     for i in range(1,size-1):
%o A259048         u.append(u[i-1]+v[i-1])
%o A259048         v.append(u[i-1]**2+v[i-1]**2)
%o A259048         a.append(u[i])
%o A259048     return a # _Anders Hellström_, Jul 10 2015
%o A259048 (PARI) first(m)={my(u=vector(m),v=vector(m));v[1]=1;u[1]=1;for(i=2,m,u[i] = u[i-1] + v[i-1];v[i] = (u[i-1])^2 + (v[i-1])^2);u;} \\ _Anders Hellström_, Aug 20 2015
%K A259048 nonn
%O A259048 1,2
%A A259048 _Morris Neene_, Jun 17 2015