A Costas array can be regarded geometrically as a set of $n$ points lying on the squares of a $n \times n$ checkerboard, such that each row or column contains only one point, and that all of the $\frac{n(n − 1)}{2}$ displacement vectors between each pair of dots are distinct. —Costas array, Wikipedia
OEIS sequence A001441 counts the "number of inequivalent Costas arrays of order $n$ under [the action of the] dihedral group [of order 8]":
1, 1, 1, 2, 6, 17, 30, 60, 100, 277, 555, 990, 1616, 2168, 2467, 2648, 2294, 1892, 1283, 810, 446, 259, 114, 25, 12, 8, 29, 89, 23
Usually combinatorial things undergo "combinatorial explosions"—it's surprising that this one grows for a bit, and then decreases again.
What is the intuition for the local (global?) maximum at $n=16$?
Are asymptotic bounds known for this sequence? In particular, should I expect a value like $a(10^{10})$ to be small?
