A201272 -id:A201272 - cp's OEIS frontend

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

R. H. Hardin, Nov 29 2011

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

			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

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

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

Main diagonal gives A201270.

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

A265005 T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with rows and columns nondecreasing.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 2, 4, 1, 1, 3, 7, 9, 1, 1, 3, 14, 29, 21, 1, 1, 4, 21, 112, 140, 51, 1, 1, 4, 41, 261, 1095, 758, 127, 1, 1, 5, 54, 846, 4919, 13009, 4448, 323, 1, 1, 5, 86, 1720, 27000, 120096, 175865, 27782, 835, 1, 1, 6, 120, 4193, 97341, 1268728, 3558888, 2647438

Offset: 1

R. H. Hardin, Nov 29 2015

Table starts
.1....1.......1.........1............1..............1..............1
.1....2.......2.........3............3..............4..............4
.1....4.......7........14...........21.............41.............54
.1....9......29.......112..........261............846...........1720
.1...21.....140......1095.........4919..........27000..........97341
.1...51.....758.....13009.......120096........1268728........8360853
.1..127....4448....175865......3558888.......76714325.....1001060834
.1..323...27782...2647438....123026475.....5732148226...155796077603
.1..835..182322..43347498...4817478608...507120480166.30055866217955
.1.2188.1245399.760869739.209081118730.51689513352516

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

R. H. Hardin, Table of n, a(n) for n = 1..128

Column 2 is A001006.
Row 2 is A004526(n+2).
Row 3 is A201272.
Row 4 is A201447.
Row 5 is A200987.
Row 7 is A201071.

cp's OEIS Frontend

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.

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