A201277 T(n,k) = number of n X k 0..2 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

3, 3, 3, 1, 5, 1, 3, 4, 4, 3, 3, 12, 7, 12, 3, 1, 16, 14, 14, 16, 1, 3, 9, 21, 85, 21, 9, 3, 3, 27, 41, 199, 199, 41, 27, 3, 1, 33, 54, 143, 556, 143, 54, 33, 1, 3, 16, 86, 740, 442, 442, 740, 86, 16, 3, 3, 48, 120, 1274, 2827, 1260, 2827, 1274, 120, 48, 3, 1, 56, 168, 759, 5680

Offset

1,1

Comments

Table starts

.3..3...1....3.....3.....1......3.......3.......1........3........3........1

.3..5...4...12....16.....9.....27......33......16.......48.......56.......25

.1..4...7...14....21....41.....54......86.....120......168......218......307

.3.12..14...85...199...143....740....1274.....759.....3416.....5312.....2746

.3.16..21..199...556...442...2827....5680....3651....19960....35039....19820

.1..9..41..143...442..1260...3113....7331...15969....32737....63942...120318

.3.27..54..740..2827..3113..27008...71704...59070...408600...894812...621910

.3.33..86.1274..5680..7331..71704..215577..200867..1537010..3717215..2850024

.1.16.120..759..3651.15969..59070..200867..613916..1755850..4655000.11705266

.3.48.168.3416.19960.32737.408600.1537010.1755850.16442049.47956581.43851889

Links

R. H. Hardin, Table of n, a(n) for n = 1..684

Formula

T(n,1) = binomial(3,n modulo 3). For a 0..z array, T(n,1) = binomial(z+1, n modulo (z+1)).

Example

Some solutions for n=7 k=5
..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..1
..0..0..0..1..1....0..0..0..0..1....0..0..0..0..2....0..0..0..1..1
..0..1..1..1..1....0..0..1..1..1....0..0..0..1..2....0..0..0..1..2
..0..1..2..2..2....1..1..2..2..2....1..1..1..1..2....0..0..1..2..2
..0..1..2..2..2....1..1..2..2..2....1..1..1..2..2....1..1..1..2..2
..0..1..2..2..2....1..1..2..2..2....1..1..2..2..2....1..1..2..2..2
..1..1..2..2..2....1..1..2..2..2....1..2..2..2..2....1..2..2..2..2

Crossrefs

Columns k=1-7 give: A169609, A201271, A201272, A201273, A201274, A201275, A201276.

Main diagonal gives A201270.

Sequence in context: A372700 A123073 A059289 * A163644 A339901 A290348

Adjacent sequences: A201274 A201275 A201276 * A201278 A201279 A201280

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 29 2011

Status

approved