A202549 T(n,k) = Number of n X k nonnegative integer arrays with each row and column an ascent sequence (interior element no greater than one plus up-steps preceding it).

1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 8, 18, 8, 1, 1, 16, 86, 86, 16, 1, 1, 32, 422, 1094, 422, 32, 1, 1, 64, 2094, 15184, 15184, 2094, 64, 1, 1, 128, 10438, 219934, 658492, 219934, 10438, 128, 1, 1, 256, 52126, 3249298, 31670778, 31670778, 3249298, 52126, 256, 1, 1, 512

Offset: 1

Author

R. H. Hardin, Dec 20 2011

Keywords

• nonn
• tabl

Comments

Table starts

.1...1.....1........1...........1...............1..................1

.1...2.....4........8..........16..............32.................64

.1...4....18.......86.........422............2094..............10438

.1...8....86.....1094.......15184..........219934............3249298

.1..16...422....15184......658492........31670778.........1605067272

.1..32..2094...219934....31670778......5534917394......1078490778110

.1..64.10438..3249298..1605067272...1078490778110....876480920594230

.1.128.52126.48427802.83391232150.222425177005132.794166642153146254

Examples

			Some solutions for n=4, k=4
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..1..1..1....0..1..1..0....0..0..1..1....0..1..1..0....0..1..0..1
..0..1..1..0....0..0..1..0....0..0..1..0....0..0..1..1....0..0..0..1
..0..1..2..0....0..1..2..1....0..0..1..1....0..1..1..1....0..1..1..2
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..144

Crossrefs

Column 2 is A000079(n-1).

Column 3 is A082685(n-1).