A032260 Number of n X n (0,1) matrices such that each row and each column is nondecreasing or nonincreasing.

2, 16, 102, 528, 2470, 11016, 47950, 205792, 874998, 3694920, 15519262, 64899456, 270415262, 1123264408, 4653525150, 19234571968, 79342610902, 326704870152, 1343120023678, 5513861152000, 22606830725598, 92580354402712, 378737813468542, 1547884976787648

Offset

1,1

Links

Eric M. Schmidt, Table of n, a(n) for n = 1..1000

Don Coppersmith, Ponder This: IBM Research Monthly Puzzles, March 2004 challenge

Formula

a(n) = 2*n*(binomial(2*n, n)-n). G.f.: 4*x/(1-4*x)^(3/2)-2*x*(1+x)/(1-x)^3. - Vladimir Baltic and Vladeta Jovovic, Jul 10 2003

Crossrefs

The number of n X n 0, 1 matrices such that each row and each column is increasing is in sequence A000984.

Cf. A000984, A062528, A045992, A016742, A086113 - A086115.

Sequence in context: A043016 A197202 A361814 * A197800 A209645 A207062

Adjacent sequences: A032257 A032258 A032259 * A032261 A032262 A032263

Keyword

nonn

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Jun 25 2003

Extensions

Extended by Vladimir Baltic and Vladeta Jovovic, Jul 10 2003

More terms from Eric M. Schmidt, May 01 2013

Status

approved