A202812 T(n,k) = Number of n X k nonnegative integer arrays with each row and column increasing from zero by 0, 1 or 2.

1, 1, 1, 1, 3, 1, 1, 6, 6, 1, 1, 10, 32, 10, 1, 1, 15, 121, 121, 15, 1, 1, 21, 356, 1177, 356, 21, 1, 1, 28, 881, 8232, 8232, 881, 28, 1, 1, 36, 1925, 43483, 146300, 43483, 1925, 36, 1, 1, 45, 3830, 185051, 1874539, 1874539, 185051, 3830, 45, 1, 1, 55, 7083, 666610

Offset: 1

Author

R. H. Hardin, Dec 24 2011

Keywords

• nonn
• tabl

Comments

Table starts:

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

.1..3.....6......10.........15............21...............28

.1..6....32.....121........356...........881.............1925

.1.10...121....1177.......8232.........43483...........185051

.1.15...356....8232.....146300.......1874539.........17870566

.1.21...881...43483....1874539......60758779.......1420586923

.1.28..1925..185051...17870566....1420586923......83834499040

.1.36..3830..666610..133496644...24496279000....3569257400553

.1.45..7083.2105474..817995997..324818660255..111459151645204

.1.55.12352.5980085.4261304129.3450301922085.2641129540510016

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..0....0..0..1....0..0..0....0..0..2....0..0..2....0..0..1
..0..0..0....0..0..2....0..2..2....0..0..1....0..2..2....0..1..2....0..0..2
..0..0..1....0..2..2....0..2..2....0..2..3....0..2..3....0..1..2....0..0..2
..0..0..1....0..2..4....0..2..2....0..2..3....0..2..4....0..2..4....0..0..2
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..312

Crossrefs

Column 2 is A000217.

Formula

Empirical: columns of T(n,k) are polynomials in n of degree k*(k-1).

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