A223777 T(n,k)=Number of nXk 0..1 arrays with rows and columns unimodal and antidiagonals nondecreasing.

2, 4, 4, 7, 12, 7, 11, 28, 28, 11, 16, 56, 78, 56, 16, 22, 101, 180, 180, 101, 22, 29, 169, 371, 461, 371, 169, 29, 37, 267, 707, 1040, 1040, 707, 267, 37, 46, 403, 1269, 2164, 2516, 2164, 1269, 403, 46, 56, 586, 2170, 4246, 5573, 5573, 4246, 2170, 586, 56, 67

Offset: 1

Author

R. H. Hardin Mar 27 2013

Keywords

• nonn
• tabl

Comments

Table starts

..2...4....7....11....16.....22.....29......37......46......56.......67

..4..12...28....56...101....169....267.....403.....586.....826.....1134

..7..28...78...180...371....707...1269....2170....3563....5650.....8692

.11..56..180...461..1040...2164...4246....7950...14308...24877....41945

.16.101..371..1040..2516...5573..11635...23230...44703...83305...150815

.22.169..707..2164..5573..12975..28346...59231..119555..234348...447489

.29.267.1269..4246.11635..28346..64256..138913..290180..589799..1170809

.37.403.2170..7950.23230..59231.138913..308895..662370.1382382..2822162

.46.586.3563.14308.44703.119555.290180..662370.1451996.3093428..6448124

.56.826.5650.24877.83305.234348.589799.1382382.3093428.6707709.14215457

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..420

Crossrefs

Column 1 is A000124

Column 2 is A223764

Formula

Empirical: columns k=1..7 are polynomials of degree 2*k for n> 0,0,0,1,2,3,4