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A332660 Alternate adding and multiplying 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 A332660 #23 May 22 2020 07:58:37
%S A332660 1,1,3,9,14,112,125,2625,2659,146245,146334,21072096,21072329,
%T A332660 7944268033,7944268643,7840993150641,7840993152238,20261126305382992,
%U A332660 20261126305387173,137066519455944225345
%N A332660 Alternate adding and multiplying 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 A332660 a(0) = 0 + 1 =  1;
%e A332660 a(1) = 1 * 1 =  1;
%e A332660 a(2) = 1 + 2 =  3;
%e A332660 a(3) = 3 * 3 =  9;
%e A332660 a(4) = 9 + 5 = 14.
%t A332660 a[0] = 1; a[n_] := a[n] = If[OddQ[n], a[n-1] * Fibonacci[n+1], a[n-1] + Fibonacci[n+1]]; Array[a, 20, 0] (* _Amiram Eldar_, Mar 28 2020 *)
%o A332660 (Python)
%o A332660 from sympy import fibonacci
%o A332660 f = [fibonacci(n) for n in range(100)]
%o A332660 def a(n):
%o A332660     out = f[0] + f[1]
%o A332660     for i in range(1, n):
%o A332660         if i%2:
%o A332660             out *= f[i+1]
%o A332660         else:
%o A332660             out += f[i+1]
%o A332660     return out
%Y A332660 Cf. A000045, A047904, A047905, A077138, A222559, A332657, A332659.
%K A332660 nonn,less
%O A332660 0,3
%A A332660 _Adnan Baysal_, Feb 18 2020