A248744 Number of different ways one can attack all squares on an n X n chessboard with n rooks.

1, 1, 6, 48, 488, 6130, 92592, 1642046, 33514112, 774478098, 19996371200, 570583424422, 17831721894912, 605743986163706, 22223926472824832, 875786473087350750, 36893467224629215232, 1654480168085245432354, 78692809748219369422848, 3956839189675526769415958

Offset: 0

Author

Stephen Penrice, Apr 09 2017

Keywords

• nonn

Comments

Number of minimum (and minimal) dominating sets in the n X n rook graph. - Eric W. Weisstein, Jun 20 2017 and Aug 02 2017

References

• A. M. Yaglom and I. M. Yaglom, Challenging Mathematical Problems with Elementary Solutions, Vol. 1: Combinatorial Analysis and Probability Theory, Dover Publications, 1987, p. 77

Links

• Eric Weisstein's World of Mathematics, Minimal Dominating Set
• Eric Weisstein's World of Mathematics, Minimum Dominating Set
• Eric Weisstein's World of Mathematics, Rook Graph

Crossrefs

Main diagonal of A290632 and of A368831.

Cf. A000142, A000312.

Programs

Maple

A248744:=n->2*n^n-n!: seq(A248744(n), n=0..25); # Wesley Ivan Hurt, Nov 30 2017

Mathematica

Table[2 n^n - n!, {n, 20}]

Formula

a(n) = 2*n^n - n!.