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).

1, 2, 4, 12, 92, 6636, 42839036, 1834614576635532, 3365810487617338033584723922844, 11328680238554850474377984661704304183660014108982249765031212

Offset: 1

Author

Morris Neene, Jun 17 2015

Keywords

• nonn

Examples

			u(2) = 2, v(2) = 2; u(3) = 4, v(3) = 8; u(4) = 12, v(4) = 80; u(5) = 92, v(5) = 6544.
		

Programs

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

Mathematica

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}]

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

Sage

def main(size):
    u=[1]; v=[1]; a=[1]
    for i in range(1,size-1):
        u.append(u[i-1]+v[i-1])
        v.append(u[i-1]**2+v[i-1]**2)
        a.append(u[i])
    return a # Anders Hellström, Jul 10 2015

Formula

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.