A229771 -id:A229771 - cp's OEIS frontend

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

R. H. Hardin, Nov 27 2016

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

			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

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

Column 1 is A000292(n+1).

Diagonal is A229771.

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]

cp's OEIS Frontend

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

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