A202756 T(n,k)=Number of nXk nonnegative integer arrays with each row and column increasing from zero by 0 or 1.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 8, 4, 1, 1, 5, 17, 17, 5, 1, 1, 6, 31, 62, 31, 6, 1, 1, 7, 51, 184, 184, 51, 7, 1, 1, 8, 78, 462, 924, 462, 78, 8, 1, 1, 9, 113, 1022, 3809, 3809, 1022, 113, 9, 1, 1, 10, 157, 2052, 13197, 26394, 13197, 2052, 157, 10, 1, 1, 11, 211, 3819, 39675

Offset: 1

Author

R. H. Hardin Dec 23 2011

Keywords

• nonn
• tabl

Comments

Table starts

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

.1..2...3....4......5........6.........7...........8............9

.1..3...8...17.....31.......51........78.........113..........157

.1..4..17...62....184......462......1022........2052.........3819

.1..5..31..184....924.....3809.....13197.......39675.......106357

.1..6..51..462...3809....26394....150777......721382......2964632

.1..7..78.1022..13197...150777...1442764....11408125.....75393424

.1..8.113.2052..39675...721382..11408125...150786848...1649287336

.1..9.157.3819.106357..2964632..75393424..1649287336..30114993376

.1.10.211.6688.259669.10720688.424992394.15057496688.455474662471

Examples

			Some solutions for n=5 k=3
..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
..0..0..0....0..0..1....0..0..0....0..1..1....0..1..1....0..0..0....0..0..0
..0..0..1....0..0..1....0..0..0....0..1..1....0..1..2....0..0..0....0..0..0
..0..0..1....0..1..1....0..0..1....0..1..2....0..1..2....0..0..0....0..0..0
..0..0..1....0..1..2....0..1..1....0..1..2....0..1..2....0..1..1....0..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..684

Crossrefs

Column 3 is A105163(n+1)

Formula

Empirical: Columns of T(n,k) are a polynomial in n of degree k*(k-1)/2.

For elements increasing by 0..d instead of 0..1, columns are a polynomial of degree d*k*(k-1)/2.