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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).

%I A333591 #10 May 28 2020 04:51:16
%S A333591 0,1,2,5,25,33,429,450,15300,15355,1366595,1366739,318450187,
%T A333591 318450564,194254844040,194254845027,310224987508119,310224987510703,
%U A333591 1297050672782249243,1297050672782256008,14197516664274574263568,14197516664274574281279
%N 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).
%e A333591 a(0) = 0 * 1 =  0;
%e A333591 a(1) = 0 + 1 =  1;
%e A333591 a(2) = 1 * 2 =  2;
%e A333591 a(3) = 2 + 3 =  5;
%e A333591 a(4) = 5 * 5 = 25.
%t A333591 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 *)
%o A333591 (Python)
%o A333591 from sympy import fibonacci
%o A333591 f = [fibonacci(n) for n in range(200)]
%o A333591 def a(n):
%o A333591     out = f[0] * f[1]
%o A333591     for i in range(1, n+1):
%o A333591         if i%2:
%o A333591             out += f[i+1]
%o A333591         else:
%o A333591             out *= f[i+1]
%o A333591     return out
%Y A333591 Cf. A000045, A047904, A047905, A077138, A222559, A332657, A332659.
%K A333591 nonn
%O A333591 0,3
%A A333591 _Adnan Baysal_, Mar 27 2020