A000519

[Jim Nastos]

On Fri, 18 Apr 2003, Brendan McKay wrote:

> Anyone have an idea about what this is?  Strictly speaking,
> each row of a Latin square has the same sum.

> ID Number: A000519
> Sequence:  1,2,3,5,7,18,43,313,7525,846992,324127859
> Name:      Number of different row sums among Latin squares of order n.

  Perhaps he meant different (main) diagonal sums? Seems to work for the 
first two entries, and let's check n=3:

I think these are the only two distinct latin squares of order 3...
(up to relabelling)
	abc	bca
	cab	cab
	bca  	abc

on first square: for a =1,2,3 we have sums 3,6,9 
on second square, no matter what the function f:{a,b,c}->{1,2,3} is, we 
get 6 (repeat), so there are 3 distinct sums.

  I'm about to fall alseep, so I won't attempt at n=4. Someone check if 
there are 5 distinct diagonal sums, please! (else I'll try it tomorrow)

Jim Nastos