A259048 - OEIS

%I #24 Sep 08 2022 08:46:13

%S 1,2,4,12,92,6636,42839036,1834614576635532,

%T 3365810487617338033584723922844,

%U 11328680238554850474377984661704304183660014108982249765031212

%N 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 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 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 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 (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 (Sage)

%o def main(size):

%o     u=[1]; v=[1]; a=[1]

%o     for i in range(1,size-1):

%o         u.append(u[i-1]+v[i-1])

%o         v.append(u[i-1]**2+v[i-1]**2)

%o         a.append(u[i])

%o     return a # _Anders Hellström_, Jul 10 2015

%o (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 nonn

%O 1,2

%A _Morris Neene_, Jun 17 2015