%I #24 Jan 14 2022 07:35:58
%S 1,1,3,8,14,32,60,128,248,512,1008,2048,4064,8192,16320,32768,65408,
%T 131072,261888,524288,1048064,2097152,4193280,8388608,16775168,
%U 33554432,67104768,134217728,268427264
%N The number of degree-n^2 polynomials over Z/2Z that can be written as f(f(x)) where f is a polynomial.
%F Conjecture:
%F a(2n) = A033991(2^(n-1)) = 4^n - 2^(n-1) for n >= 1;
%F a(2n+1) = 2^(2n+1) for n >= 1.
%F Conjecture from _Hugo Pfoertner_, Jan 09 2022: Terms starting at 3 coincide with {A156232}/8.
%e For n = 2, there are a(2) = 3 degree 4 polynomials of the form f(f(x)):
%e x^4 = f(f(x)) when f(x) = x^2 or f(x) = x^2 + 1,
%e x^4 + x = f(f(x)) when f(x) = x^2 + x, and
%e x^4 + x + 1 = f(f(x)) when f(x) = x^2 + x + 1.
%Y Cf. A033991, A156212, A156232.
%K nonn,more
%O 0,3
%A _Peter Kagey_, Jan 03 2022
%E a(0) prepended and a(11)-a(28) from _Martin Ehrenstein_, Jan 14 2022