[seqfan] Re: Nathaniel Johnston's "orderings of pairs" A237749.

[Hans Havermann]

"... the number of combinatorially different Golomb rulers with a given number of markings (this sequence starts with 1, 2, 10, 114, 2608, and 107498)."

The sequence appears in Tu Pham's May 2011 thesis (Enumeration of Golomb Rulers):

"This means the projected region is precisely described by the hyperplane arrangement H(m). Hence we conclude the projected region is a region of G(m).

By using a program to compute the number of regions of an inside-out polytope written by Andrew Van Herick[3], we were able to compute the number of regions of G(m) where m ranges from 1 to 6.

m   R(m)
1      1
2      2
3     10
4    114
5   2608
6 107498

Table 3.1: The number of regions of G(m)."

The reference [3] is to Matthias Beck and Andrew van Herick, Enumeration of 4 × 4 magic squares, Math. Comp. 80 (2011), no. 273, 617–621. MR 2728997.