A201451 T(n,k)=Number of nXk 0..3 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

4, 6, 6, 4, 2, 4, 1, 21, 21, 1, 4, 9, 52, 9, 4, 6, 56, 29, 29, 56, 6, 4, 13, 246, 112, 246, 13, 4, 1, 110, 701, 261, 261, 701, 110, 1, 4, 32, 844, 846, 4544, 846, 844, 32, 4, 6, 198, 426, 1720, 22324, 22324, 1720, 426, 198, 6, 4, 41, 2478, 4193, 45532, 16334, 45532, 4193

Offset: 1

Author

R. H. Hardin Dec 01 2011

Keywords

• nonn
• tabl

Comments

Table starts

.4...6....4.....1.......4.......6........4........1..........4..........6

.6...2...21.....9......56......13......110.......32........198.........41

.4..21...52....29.....246.....701......844......426.......2478.......5990

.1...9...29...112.....261.....846.....1720.....4193.......8065......16693

.4..56..246...261....4544...22324....45532....32314.....313710....1126721

.6..13..701...846...22324...16334...363693...211755....3708666....1743841

.4.110..844..1720...45532..363693..1129682..1136762...16354832...80822317

.1..32..426..4193...32314..211755..1136762..5464208...23238776...89540916

.4.198.2478..8065..313710.3708666.16354832.23238776..458459214.3056235023

.6..41.5990.16693.1126721.1743841.80822317.89540916.3056235023.2605975384

Examples

			Some solutions for n=10 k=3
..0..0..0....0..0..0....0..0..1....0..0..1....0..0..0....0..1..1....0..0..1
..0..1..1....0..0..1....0..0..2....0..0..1....0..0..0....0..1..1....0..0..2
..0..1..2....0..1..1....0..0..2....0..0..2....0..1..1....0..1..1....0..1..2
..0..1..2....0..1..1....0..1..2....0..1..2....1..1..2....0..1..2....0..1..2
..0..1..2....1..1..2....1..1..3....0..1..2....1..2..3....0..2..2....0..1..3
..1..1..3....2..2..2....1..1..3....1..2..2....1..2..3....0..2..2....1..2..3
..1..2..3....2..2..3....1..1..3....1..3..3....1..2..3....0..3..3....1..2..3
..2..2..3....2..2..3....2..2..3....1..3..3....1..2..3....2..3..3....1..2..3
..2..2..3....3..3..3....2..2..3....2..3..3....2..3..3....2..3..3....1..3..3
..3..3..3....3..3..3....2..3..3....2..3..3....2..3..3....2..3..3....2..3..3
		

Links

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

Formula

T(n,1) = binomial(4,n modulo 4). For a 0..z array, T(n,1) = binomial(z+1, n modulo (z+1)).