A087518 Number of arrangements of 1..n^2 in n X n array with exactly one local maximum.

1, 16, 29568, 35704394880, 88366736882654697600

Offset: 1

Author

R. H. Hardin, Oct 23 2003

Keywords

• nonn
• nice

Comments

Neighbors of a cell are only considered in the X and Y directions.

Number of ways to dig an n X n hole where each cell is at a different depth and water will collect in just one puddle.

Computed using a C program, brute force enumeration except using a cache of old results to cut off the search tree. For many related problems however, R. H. Hardin has coded them in S/R (which is COSPAN's language).

Examples

			For n=2, 12 has only one local max., whereas 13 has two and is excluded.
........ 34 ................................ 42
		

Crossrefs

For the same problem with an n X 1 array see A000079. With no shape constraint, see A007846. Cf. A087519. Main diagonal of A087783.