No of sudokus, A107739

[hv at crypt.org]

"N. J. A. Sloane" <njas at research.att.com> wrote:
:
:Sequence A107739, submitted by Richard McNair, has a long entry,
:beginning:
:
:%I A107739
:%S A107739 1,2,288,6670903752021072936960
:%N A107739 Number of valid sudokus of order 2n.
:%H A107739 Wikipedia, <a href="http://en.wikipedia.org/wiki/Sudoku">Sudoku</a>
:...
:
:The definition looks wrong to me, but I don't
:know anything about these puzzles.  I'm guessing that
:the description should really "the number of order n"
:and that 6670903752021072936960 is the number of order 3,
:which is the standard 9 X 9 puzzle seen in newspapers.
:
:Can someone who knows about these things confirm this?

My best guess is a typo for "order n^2" - what you refer to as order 3
requires a (3^2 x 3^2) grid. But calling it order 3 seems reasonable,
or ducking that and calling it "number of valid sudokus on an
n^2 x n^2 grid".

It also isn't clear whether it is counting the number of complete grids
possible, or the number of valid games: ie, the number of partial grids
available which suffice to determine the complete grid. a(1)=2 implies
the latter - there is one grid, consisting of a single '1', and that '1'
can be either supplied or blank. But a(2)=288 suggests the first meaning,
since that is how many 2^2 x 2^2 complete grids there are.

So I think the numbers are wrong whatever definition we end up with.

Hugo