[seqfan] Permutations whose sum mod n is also a permutation

[Ron Hardin]

Quickie computation, offset 1

1,0,12,0,960,0,337680,0,367597440
Number of lexicographically ordered pairs of permutations of 0..(n-1) such that 
their sum mod n is also a permutation of 0..(n-1)

for n=3
permutation 1
permutation 2
sum (mod 3)

1
 0 1 2
 0 1 2
 0 2 1
2
 0 2 1
 0 2 1
 0 1 2
3
 0 1 2
 1 2 0
 1 0 2
4
 0 2 1
 1 0 2
 1 2 0
5
 0 1 2
 2 0 1
 2 1 0
6
 0 2 1
 2 1 0
 2 0 1
7
 1 0 2
 1 0 2
 2 0 1
8
 1 2 0
 1 2 0
 2 1 0
9
 1 0 2
 2 1 0
 0 1 2
10
 1 2 0
 2 0 1
 0 2 1
11
 2 0 1
 2 0 1
 1 0 2
12
 2 1 0
 2 1 0
 1 2 0

unlikely to get more terms except for a very good guess at n=10, at least with 
the current method.

 rhhardin at mindspring.com
rhhardin at att.net (either)