The number of valid crossword puzzles for odd-length grids up to size 21 has recently been computed (http://oeis.org/A323839). Valid rows up to size 5,000 and symmetric rows up to 10,000 are at http://oeis.org/A130578 and http://oeis.org/A131524.

NOTE: the numbers in the first list are a little lower than the totals computed by Tom Terwillinger posted in the May/June 2009 issue of Puzzle Corner as valid crosswords require that all open squares are contained in a row AND column of at least three open squares (the problem used OR).