A333591 Alternate multiplying and adding Fibonacci numbers: a(0) = F(0) * F(1), for n >= 0, a(2n+1) = a(2n) + F(2n+2), a(2n+2) = a(2n+1) * F(2n+3).

0, 1, 2, 5, 25, 33, 429, 450, 15300, 15355, 1366595, 1366739, 318450187, 318450564, 194254844040, 194254845027, 310224987508119, 310224987510703, 1297050672782249243, 1297050672782256008, 14197516664274574263568, 14197516664274574281279

Offset: 0

Author

Adnan Baysal, Mar 27 2020

Keywords

• nonn

Examples

			a(0) = 0 * 1 =  0;
a(1) = 0 + 1 =  1;
a(2) = 1 * 2 =  2;
a(3) = 2 + 3 =  5;
a(4) = 5 * 5 = 25.
		

Crossrefs

Cf. A000045, A047904, A047905, A077138, A222559, A332657, A332659.

Programs

Mathematica

a[0] = 0; a[n_] := a[n] = If[EvenQ[n], a[n-1] * Fibonacci[n+1], a[n-1] + Fibonacci[n+1]]; Array[a, 22, 0] (* Amiram Eldar, Mar 28 2020 *)

Python

from sympy import fibonacci
f = [fibonacci(n) for n in range(200)]
def a(n):
    out = f[0] * f[1]
    for i in range(1, n+1):
        if i%2:
            out += f[i+1]
        else:
            out *= f[i+1]
    return out