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A356891 a(n) = a(n-1) * a(n-2) + 1 if n is even, otherwise a(n) = a(n-3) + 1, with a(0) = a(1) = 1.

%I A356891 #26 Nov 06 2022 08:40:18
%S A356891 1,1,2,2,5,3,16,6,97,17,1650,98,161701,1651,266968352,161702,
%T A356891 43169316455105,266968353,11524841314155180292066,43169316455106,
%U A356891 497519521785644682185076928856988997,11524841314155180292067
%N A356891 a(n) = a(n-1) * a(n-2) + 1 if n is even, otherwise a(n) = a(n-3) + 1, with a(0) = a(1) = 1.
%H A356891 J. Conrad, <a href="/A356891/b356891.txt">Table of n, a(n) for n = 0..34</a>
%e A356891 For n=2, a(2) = a(0) * a(1) + 1 = 2.
%e A356891 For n=3, a(3) = a(0) + 1 = 2.
%e A356891 For n=4, a(4) = a(3) * a(2) + 1 = 5.
%t A356891 a[n_] := a[n] = If[EvenQ[n], a[n - 1]*a[n - 2], a[n - 3]] + 1; a[0] = a[1] = 1; Array[a, 22, 0] (* _Amiram Eldar_, Sep 10 2022 *)
%o A356891 (Python)
%o A356891 def A356891(length):
%o A356891     output = [1] * length
%o A356891     for n in range(2, length):
%o A356891         output[n] += output[n-3] if n % 2 else output[n-1] * output[n-2]
%o A356891     return output
%Y A356891 Cf. A007660.
%K A356891 nonn
%O A356891 0,3
%A A356891 _J. Conrad_, Sep 02 2022