A368061 The number of ways to place one pawn and n+1 nonattacking queens on an n X n chessboard, unchanged by 180-degree rotation.

0, 0, 0, 0, 0, 0, 1, 0, 5, 0, 18, 0, 50, 0, 652, 0, 4260, 0, 25134, 0, 238098, 0, 2492304, 0, 25389294

Offset: 1

Author

Don Knuth, Dec 10 2023

Keywords

• nonn
• more

Comments

n must be odd, and the pawn must be in the center.

Examples

			For n=7 the a(7)=1 solution is
  . . Q . . . .
  . . . . . Q .
  . . . Q . . .
  Q . . P . . Q
  . . . Q . . .
  . Q . . . . .
  . . . . Q . .
		

Crossrefs

A103330 counts all solutions; A103331 counts them with symmetry removed.

Formula

A103330(n) = 8*A103331(n) - 4*a(n).