A278727 T(n,k)=Number of nXk 0..3 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order.

4, 10, 10, 20, 60, 20, 35, 275, 275, 35, 56, 1050, 3232, 1050, 56, 84, 3492, 33466, 33466, 3492, 84, 120, 10401, 306070, 1058494, 306070, 10401, 120, 165, 28288, 2487889, 30942600, 30942600, 2487889, 28288, 165, 220, 71266, 18151220, 815294800

Offset

1,1

Comments

Table starts

...4.....10........20............35.................56.....................84

..10.....60.......275..........1050...............3492..................10401

..20....275......3232.........33466.............306070................2487889

..35...1050.....33466.......1058494...........30942600..............815294800

..56...3492....306070......30942600.........3062815568...........279368748599

..84..10401...2487889.....815294800.......279368748599.........90462380211862

.120..28288..18151220...19328645044.....23161560633508......26947618206791521

.165..71266.120104810..414671691083...1747727428639023....7361981179311574929

.220.168155.727684612.8109321869307.120668752462156921.1850980180963910285369

Links

R. H. Hardin, Table of n, a(n) for n = 1..111

Formula

Empirical for column k:

k=1: a(n) = (1/6)*n^3 + 1*n^2 + (11/6)*n + 1

k=2: [polynomial of degree 12]

k=3: [polynomial of degree 45]

Example

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

Crossrefs

Column 1 is A000292(n+1).

Diagonal is A229771.

Sequence in context: A352753 A310336 A227060 * A184129 A202581 A201729

Adjacent sequences: A278724 A278725 A278726 * A278728 A278729 A278730

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 27 2016

Status

approved