A200777 T(n,k)=Number of nXk 0..2 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

3, 3, 3, 2, 5, 2, 7, 5, 5, 7, 9, 20, 13, 20, 9, 6, 37, 31, 31, 37, 6, 22, 31, 77, 342, 77, 31, 22, 30, 144, 217, 1368, 1368, 217, 144, 30, 20, 273, 553, 1806, 7725, 1806, 553, 273, 20, 75, 218, 1438, 18801, 13422, 13422, 18801, 1438, 218, 75, 105, 1054, 3849, 66784, 194535

Offset: 1

Author

R. H. Hardin Nov 22 2011

Keywords

• nonn
• tabl

Comments

Table starts

..3....3....2......7........9.........6..........22...........30............20

..3....5....5.....20.......37........31.........144..........273...........218

..2....5...13.....31.......77.......217.........553.........1438..........3849

..7...20...31....342.....1368......1806.......18801........66784.........80772

..9...37...77...1368.....7725.....13422......194535.......980702.......1678693

..6...31..217...1806....13422.....91755......633413......4472626......30905995

.22..144..553..18801...194535....633413....17965438....171117355.....537341613

.30..273.1438..66784...980702...4472626...171117355...2189118202....9237040535

.20..218.3849..80772..1678693..30905995...537341613...9237040535..159001066390

.75.1054.9634.855668.24878620.209517906.14614583388.342978784324.2722231659577

Examples

			Some solutions for n=6 k=4
..0..0..0..0....0..0..1..1....0..0..0..0....0..0..0..0....0..0..0..0
..0..1..2..1....0..0..1..2....0..1..2..1....0..0..2..2....0..0..2..1
..0..2..1..2....0..0..1..2....0..1..2..1....0..0..1..1....0..1..2..1
..0..1..1..2....0..1..1..2....0..1..2..1....1..1..1..2....0..1..2..2
..0..1..2..2....0..2..1..2....0..2..2..2....1..1..2..2....1..1..2..2
..1..1..2..2....1..2..2..2....1..1..2..2....1..2..2..2....1..1..2..2
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..178

Crossrefs

Column 1 includes A003409((n+1)/3) and A000984(n/3)