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A201277 T(n,k)=Number of nXk 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 8
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 (list; table; graph; refs; listen; history; text; internal format)
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

Sequence in context: A256736 A123073 A059289 * A163644 A290348 A014465

Adjacent sequences:  A201274 A201275 A201276 * A201278 A201279 A201280

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Nov 29 2011

STATUS

approved

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Last modified February 27 08:51 EST 2020. Contains 332301 sequences. (Running on oeis4.)