%I #29 Sep 08 2022 08:46:15

%S 1,1,2,4,6,36,42,1764,1806,3261636,3263442,10650053687364,

%T 10650056950806,113423713055411194304049636,

%U 113423713055421844361000442,12864938683278671740537145884937248491231415124195364,12864938683278671740537145998360961546653259485195806

%N a(0) = a(1) = 1; thereafter a(n) = a(n-1) + a(n-2) if n is even, otherwise a(n) = a(n-1)^2.

%C The first bisection is A007018, the second bisection is A174864 (with an only initial 1).

%C After 2, all terms belong to A238411.

%F a(n) = ( 1 + Sum_{k=0..floor(n/2)-1} a(2*k+1) )^(3-(-1)^n)/2 for n>1.

%t a[n_] := If[OddQ@n, a[n - 1] + a[n - 2], a[n - 1]^2]; a[0] = 1; Array[a, 17]

%o (Magma) [n le 2 select 1 else IsEven(n) select Self(n-1)^2 else Self(n-1)+Self(n-2): n in [1..20]];

%Y Cf. A007018, A174864, A238411.

%K nonn

%O 0,3

%A _Vincenzo Librandi_, Feb 23 2016

%E Edited and extended by _Bruno Berselli_, Feb 25 2016