A223933 T(n,k)=Number of nXk 0..2 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.

3, 9, 9, 22, 54, 22, 46, 218, 218, 46, 86, 698, 1116, 698, 86, 148, 1915, 4498, 4498, 1915, 148, 239, 4690, 15791, 21334, 15791, 4690, 239, 367, 10511, 49646, 86439, 86439, 49646, 10511, 367, 541, 21919, 142177, 316136, 386495, 316136, 142177, 21919, 541

Offset: 1

Author

R. H. Hardin Mar 29 2013

Keywords

• nonn
• tabl

Comments

Table starts

...3.....9......22.......46........86........148........239.........367

...9....54.....218......698......1915.......4690......10511.......21919

..22...218....1116.....4498.....15791......49646.....142177......375777

..46...698....4498....21334.....86439.....316136....1065625.....3337831

..86..1915...15791....86439....386495....1548633....5773556....20277077

.148..4690...49646...316136...1548633....6621074...26250443....98910688

.239.10511..142177..1065625...5773556...26250443..108796955...427868778

.367.21919..375777..3337831..20277077...98910688..427868778..1735753333

.541.43045..926559..9773219..67308910..356869229.1623374603..6788778441

.771.80334.2150622.26903878.211460339.1233491661.5968786086.25890527027

Examples

			Some solutions for n=3 k=4
..0..0..2..1....0..0..0..1....0..1..1..2....2..2..2..2....1..1..0..0
..0..1..1..2....0..2..1..1....0..0..2..2....1..2..2..2....1..1..1..2
..0..1..1..2....0..2..2..2....0..0..2..2....1..2..2..2....0..1..2..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..180

Crossrefs

Column 1 is A223718

Formula

Empirical: columns k=1..6 are polynomials of degree 4*k for n>0,0,3,6,9,12