The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.

a(n) is the maximum number k of queens that can be placed on an n X n chessboard such that, for each number j in 0..k-1, there is a queen attacking exactly j unoccupied squares.

On the 6 X 6 board in the illustration (see Example), each square containing a number is occupied by a queen, and the number in that square is the number of unoccupied squares attacked by that queen. (Each square with no number is unoccupied.)