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A087518 Number of arrangements of 1..n^2 in n X n array with exactly one local maximum. 3
1, 16, 29568, 35704394880, 88366736882654697600 (list; graph; refs; listen; history; internal format)
OFFSET

1,2

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).

EXAMPLE

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.

Sequence in context: A070904 A159427 A017416 * A017548 A185141 A087586

Adjacent sequences:  A087515 A087516 A087517 * A087519 A087520 A087521

KEYWORD

nonn,nice

AUTHOR

R. H. Hardin (rhhardin(AT)att.net), Oct 23 2003

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Last modified February 14 14:07 EST 2012. Contains 205623 sequences.