A189837 Number of ways to place n nonattacking composite pieces rook + rider[1,2] on an n X n chessboard.

1, 2, 2, 8, 12, 22, 58, 276, 648, 2304, 6508, 24528, 96402, 466922, 2271738, 13723826, 76579326, 512425626, 3281233020, 24654941268, 175398054696

Offset: 1

Author

Vaclav Kotesovec, Apr 29 2011

Keywords

• nonn
• hard

Comments

(In fairy chess the rider [1,2] is called a Nightrider, Rook + Nightrider = Waran.)

a(n) is also the number of permutations p of 1,2,...,n satisfying |p(i+k) - p(i)| <> 2k AND |p(j+2k) - p(j)| <> k for all i >= 1, j >= 1, k >= 1, i+k <= n, j+2k <= n.

Links

• V. Kotesovec, Number of ways of placing non-attacking queens, kings, bishops and knights (in English and Czech).
• Wikipedia, Fairy chess piece

Crossrefs

Cf. A102388, A000170.