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

1,1

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

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)).

Example

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

Crossrefs

Sequence in context: A349701 A344777 A191761 * A200352 A286720 A201393

Adjacent sequences: A201448 A201449 A201450 * A201452 A201453 A201454

Keyword

nonn,tabl

Author

R. H. Hardin Dec 01 2011

Status

approved