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.

  If I can divert from this question for a moment...
There are a few sequences numbering the equivalence classes of latin 
squares for various definitions of equivalence... How come there is no 
sequence for the number latin squares up to isomorphism, where an 
isomorphism here is just any permutation of labels.
  There would be just 1 latin square of order 1.
  There would be just 1 latin square of order 2:

12	is isomorphic to	21
21				12

because they both have the form
	AB
	BA

  There would be just 2 latin squares of order 3:

ABC	ABC
CAB	BCA
BCA	CAB

  So is no sequence counting a type of latin square that has 1,1,2 for 
index 1,2,3.
  If I'm not mistaken, don't distinct transversal designs map to distinct 
latin squares (where the meaning "distinct latin squares" is in the sense 
above.) The encyclopedia seems to have no data counting transversal 
designs at all.

Jim Nastos