A120331 Number of polynomials in two noncommuting variables over the field F_2 having complexity or rank n.
1, 1, 6, 72, 1776, 89280, 9065472, 1850148864, 757046525952, 620298979246080, 1017126921430892544, 3336658943759213395968, 21894988380633154342354944, 287369531352172835754234347520, 7543680108676972971562235527692288
Offset: 0
Keywords
Examples
The six polynomials corresponding to a(2) are: X, Y, X+Y, 1+X, 1+Y, 1+X+Y.
Links
- R. Bacher, Table of n, a(n) for n = 0..24
- R. Bacher, The special subgroup of invertible non-commutative rational power series as a metric group, arXiv:0804.1092
Crossrefs
Cf. A137342.
Formula
The reference contains a somewhat complicated formula.