A000519
Jim Nastos
nastos at cs.ualberta.ca
Fri Apr 18 13:57:09 CEST 2003
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
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