The OEIS is supported by the many generous donors to the OEIS Foundation.

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

1

`%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
`