A120331 - OEIS

%I #13 Apr 03 2015 19:22:05

%S 1,1,6,72,1776,89280,9065472,1850148864,757046525952,620298979246080,

%T 1017126921430892544,3336658943759213395968,

%U 21894988380633154342354944,287369531352172835754234347520,7543680108676972971562235527692288

%N Number of polynomials in two noncommuting variables over the field F_2 having complexity or rank n.

%H R. Bacher, <a href="/A120331/b120331.txt">Table of n, a(n) for n = 0..24</a>

%H R. Bacher, <a href="http://arxiv.org/abs/0804.1092">The special subgroup of invertible non-commutative rational power series as a metric group</a>, arXiv:0804.1092

%F The reference contains a somewhat complicated formula.

%e The six polynomials corresponding to a(2) are: X, Y, X+Y, 1+X, 1+Y, 1+X+Y.

%Y Cf. A137342.

%K nonn

%O 0,3

%A _Roland Bacher_, Apr 29 2008