A202735 T(n,k)=Number of nXk nonnegative integer arrays with each row and column an ascent sequence (interior element no greater than one plus up-steps preceding it) and the lower right element equal to min(n,k)-1

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 4, 2, 4, 1, 1, 8, 14, 14, 8, 1, 1, 16, 78, 12, 78, 16, 1, 1, 32, 406, 462, 462, 406, 32, 1, 1, 64, 2062, 10296, 304, 10296, 2062, 64, 1, 1, 128, 10374, 184848, 97794, 97794, 184848, 10374, 128, 1, 1, 256, 51998, 3010632, 12219684, 44976

Offset

1,8

Comments

Table starts

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

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

.1...2......2........14............78...............406..................2062

.1...4.....14........12...........462.............10296................184848

.1...8.....78.......462...........304.............97794..............12219684

.1..16....406.....10296.........97794.............44976.............182593546

.1..32...2062....184848......12219684.........182593546..............51871384

.1..64..10374...3010632....1002070158......171227525652.........4025241096124

.1.128..51998..46867734...66418851994....82937584072426.....36422682546205910

.1.256.260246.714602604.3938900557370.28117713663244916.131056226079716655758

Links

R. H. Hardin, Table of n, a(n) for n = 1..161

Example

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..0..1....0..1..1..1....0..1..0..1....0..0..1..1....0..0..1..1
..0..1..1..2....0..1..0..2....0..0..1..2....0..1..2..2....0..1..1..2
..0..1..2..3....0..1..2..3....0..1..2..3....0..1..2..3....0..1..2..3

Crossrefs

Sequence in context: A210481 A217209 A233307 * A343862 A116595 A128315

Adjacent sequences: A202732 A202733 A202734 * A202736 A202737 A202738

Keyword

nonn,tabl

Author

R. H. Hardin Dec 23 2011

Status

approved