A200990 T(n,k)=Number of nXk 0..4 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

5, 10, 10, 10, 10, 10, 5, 20, 20, 5, 1, 79, 92, 79, 1, 5, 21, 537, 537, 21, 5, 10, 226, 140, 1225, 140, 226, 10, 10, 157, 3157, 1095, 1095, 3157, 157, 10, 5, 227, 3604, 15023, 4919, 15023, 3604, 227, 5, 1, 678, 6692, 95845, 27000, 27000, 95845, 6692, 678, 1, 5, 120

Offset: 1

Author

R. H. Hardin Nov 25 2011

Keywords

• nonn
• tabl

Comments

Table starts

..5..10....10......5.......1........5.........10..........10...........5

.10..10....20.....79......21......226........157.........227.........678

.10..20....92....537.....140.....3157.......3604........6692.......26168

..5..79...537...1225....1095....15023......95845......268375......325061

..1..21...140...1095....4919....27000......97341......383172.....1188521

..5.226..3157..15023...27000...752271....8434277....39361323....80878071

.10.157..3604..95845...97341..8434277...29555346...171588826..1801771085

.10.227..6692.268375..383172.39361323..171588826..1278883650.16557969007

..5.678.26168.325061.1188521.80878071.1801771085.16557969007.65182166083

..1.120..5408.168262.3704820.64001290..853004113..9528745293.89750034774

Examples

			Some solutions for n=5 k=3
..0..1..2....0..0..2....0..1..2....0..0..1....0..0..0....0..1..1....0..0..0
..0..1..3....0..1..2....0..1..2....0..1..3....1..1..2....0..1..2....1..1..1
..0..1..4....1..3..4....0..1..2....1..2..3....1..2..3....0..3..3....2..3..4
..2..2..4....1..3..4....3..3..4....2..2..3....2..3..3....2..3..4....2..3..4
..3..3..4....2..3..4....3..4..4....4..4..4....4..4..4....2..4..4....2..3..4
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..199

Crossrefs

Column 1 for a 0..z array is binomial(z+1,n modulo (z+1))

Formula

T(n,1) = binomial(5,n modulo 5). For a 0..z array, T(n,1) = binomial(z+1, n modulo (z+1)).