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

Author

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

Keywords

• nonn

Links

• Eric M. Schmidt, Table of n, a(n) for n = 1..1000
• Don Coppersmith, Ponder This: IBM Research Monthly Puzzles, March 2004 challenge

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.

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

Extensions

Extended by Vladimir Baltic and Vladeta Jovovic, Jul 10 2003

More terms from Eric M. Schmidt, May 01 2013