cp's OEIS Frontend

A350520 The number of degree-n^2 polynomials over Z/2Z that can be written as f(f(x)) where f is a polynomial.

%I A350520 #24 Jan 14 2022 07:35:58
%S A350520 1,1,3,8,14,32,60,128,248,512,1008,2048,4064,8192,16320,32768,65408,
%T A350520 131072,261888,524288,1048064,2097152,4193280,8388608,16775168,
%U A350520 33554432,67104768,134217728,268427264
%N A350520 The number of degree-n^2 polynomials over Z/2Z that can be written as f(f(x)) where f is a polynomial.
%F A350520 Conjecture:
%F A350520   a(2n) = A033991(2^(n-1)) = 4^n - 2^(n-1) for n >= 1;
%F A350520   a(2n+1) = 2^(2n+1) for n >= 1.
%F A350520 Conjecture from _Hugo Pfoertner_, Jan 09 2022: Terms starting at 3 coincide with {A156232}/8.
%e A350520 For n = 2, there are a(2) = 3 degree 4 polynomials of the form f(f(x)):
%e A350520   x^4         = f(f(x)) when f(x) = x^2 or f(x) = x^2 + 1,
%e A350520   x^4 + x     = f(f(x)) when f(x) = x^2 + x, and
%e A350520   x^4 + x + 1 = f(f(x)) when f(x) = x^2 + x + 1.
%Y A350520 Cf. A033991, A156212, A156232.
%K A350520 nonn,more
%O A350520 0,3
%A A350520 _Peter Kagey_, Jan 03 2022
%E A350520 a(0) prepended and a(11)-a(28) from _Martin Ehrenstein_, Jan 14 2022