A278807 T(n,k)=Number of nXk 0..2 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order.

3, 6, 6, 10, 22, 10, 15, 63, 63, 15, 21, 154, 322, 154, 21, 28, 336, 1439, 1439, 336, 28, 36, 672, 5767, 12958, 5767, 672, 36, 45, 1254, 20972, 110455, 110455, 20972, 1254, 45, 55, 2211, 69834, 870473, 2179956, 870473, 69834, 2211, 55, 66, 3718, 214774, 6275546

Offset: 1

Author

R. H. Hardin, Nov 28 2016

Keywords

• nonn
• tabl

Comments

Table starts

..3....6......10.........15............21...............28.................36

..6...22......63........154...........336..............672...............1254

.10...63.....322.......1439..........5767............20972..............69834

.15..154....1439......12958........110455...........870473............6275546

.21..336....5767.....110455.......2179956.........41299256..........725674326

.28..672...20972.....870473......41299256.......1976588468........89730161098

.36.1254...69834....6275546.....725674326......89730161098.....10811999412826

.45.2211..214774...41370842...11698232451....3776527762052...1224101415304069

.55.3718..615120..250517485..172994405326..146582077597322.128795068372302728

.66.6006.1653047.1402100369.2356249442222.5255148833158068

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..127

Crossrefs

Diagonal is A229770.

Column 1 is A000217(n+1).

Column 2 is A257200(n+1).

Formula

Empirical for column k:

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

k=2: [polynomial of degree 6]

k=3: [polynomial of degree 16]

k=4: [polynomial of degree 44]