A269265 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.

1, 1, 2, 4, 6, 36, 42, 1764, 1806, 3261636, 3263442, 10650053687364, 10650056950806, 113423713055411194304049636, 113423713055421844361000442, 12864938683278671740537145884937248491231415124195364, 12864938683278671740537145998360961546653259485195806

Offset: 0

Author

Vincenzo Librandi, Feb 23 2016

Keywords

• nonn

Comments

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

After 2, all terms belong to A238411.

Crossrefs

Cf. A007018, A174864, A238411.

Programs

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]];

Mathematica

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

Formula

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

Extensions

Edited and extended by Bruno Berselli, Feb 25 2016