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

1,1

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

Links

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

Formula

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

Example

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

Crossrefs

Column 1 is A223718

Sequence in context: A203600 A099720 A183149 * A224057 A224310 A224374

Adjacent sequences: A223930 A223931 A223932 * A223934 A223935 A223936

Keyword

nonn,tabl

Author

R. H. Hardin Mar 29 2013

Status

approved