1,2

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, Ron Hardin has coded them in S/R (which is COSPAN's language).

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

........ 34 ................................ 42

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

Sequence in context: A017296 A070904 A017416 this_sequence A017548 A087586 A105312

Adjacent sequences: A087515 A087516 A087517 this_sequence A087519 A087520 A087521

nonn,nice

Ron Hardin (rhh(AT)cadence.com), Oct 23 2003