A096970 Number of ways to number the cells of an n X n square grid with 1,2,3,...,n^2 so that successive integers are in the same row or column.

1, 8, 1512, 22394880, 50657369241600, 28606505102329400524800, 5959275438217048853558620520448000

Offset

1,2

Comments

Suggested by Leroy Quet, Jul 05 2004.

For n >= 2, number of (directed) Hamiltonian paths on the n X n rook graph. - Eric W. Weisstein, Dec 16 2013

Links

Table of n, a(n) for n=1..7.

Eric Weisstein's World of Mathematics, Hamiltonian Path

Eric Weisstein's World of Mathematics, Rook Graph

Index entries for sequences related to graphs, Hamiltonian

Example

Among the 4 X 4 grids counted is:
1   2  3 10
15  6  5 11
14 13  4 12
16  7  8  9

Crossrefs

Cf. A096969, A269561, A269565.

Sequence in context: A172938 A252176 A252763 * A248386 A114617 A162014

Adjacent sequences: A096967 A096968 A096969 * A096971 A096972 A096973

Keyword

nonn,more,hard

Author

John W. Layman, Jul 16 2004

Extensions

a(5) from Eric W. Weisstein, Dec 28 2013

a(6)-a(7) from Andrew Howroyd, Feb 29 2016

Status

approved