A145238 1/3 of the number of 3-colorings of an n X n array symmetric about both diagonal and antidiagonal.

1, 2, 8, 24, 144, 648, 5904, 40392, 561744, 5871528, 124982208, 2000735640, 65289654720, 1603001126808, 80277953271984, 3025716988718520, 232703590361105952, 13472417658155610888, 1592017750060187494896