A278778 T(n,k)=Number of nXk 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly two mistakes.

0, 0, 0, 0, 2, 0, 1, 20, 20, 1, 6, 117, 266, 117, 6, 21, 503, 1972, 1972, 503, 21, 56, 1750, 10784, 19750, 10784, 1750, 56, 126, 5209, 48501, 150085, 150085, 48501, 5209, 126, 252, 13751, 189595, 955347, 1673658, 955347, 189595, 13751, 252, 462, 33000

Offset: 1

Author

R. H. Hardin, Nov 28 2016

Keywords

• nonn
• tabl

Comments

Table starts

...0.....0.......0.........1...........6............21..............56

...0.....2......20.......117.........503..........1750............5209

...0....20.....266......1972.......10784.........48501..........189595

...1...117....1972.....19750......150085........955347.........5355983

...6...503...10784....150085.....1673658......16205001.......141166787

..21..1750...48501....955347....16205001.....251740932......3634987413

..56..5209..189595...5355983...141166787....3634987413.....90752836672

.126.13751..665212..27218249..1126917480...48847405083...2155380363189

.252.33000.2138149.127644118..8340736743..611199661843..48042054699217

.462.73282.6384894.559023840.57745890265.7140933364136.999491681597761

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..219

Crossrefs

Column 1 is A000389(n+1).

Formula

Empirical for column k:

k=1: a(n) = (1/120)*n^5 - (1/24)*n^4 + (1/24)*n^3 + (1/24)*n^2 - (1/20)*n

k=2: [polynomial of degree 10]

k=3: [polynomial of degree 19]

k=4: [polynomial of degree 36]

k=5: [polynomial of degree 69]

k=6: [polynomial of degree 134]