A278627 T(n,k)=Number of nXk 0..2 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly one mistake.

0, 3, 3, 16, 46, 16, 51, 357, 357, 51, 126, 1952, 4754, 1952, 126, 266, 8518, 49503, 49503, 8518, 266, 504, 31605, 439446, 1069536, 439446, 31605, 504, 882, 103546, 3438414, 21121532, 21121532, 3438414, 103546, 882, 1452, 307087, 24103803

Offset: 1

Author

R. H. Hardin, Nov 24 2016

Keywords

• nonn
• tabl

Comments

Table starts

....0......3........16............51..............126.................266

....3.....46.......357..........1952.............8518...............31605

...16....357......4754.........49503...........439446.............3438414

...51...1952.....49503.......1069536.........21121532...........387542112

..126...8518....439446......21121532........978005050.........43853346948

..266..31605...3438414.....387542112......43853346948.......4902306226424

..504.103546..24103803....6594175430....1892563134910.....540194658701142

..882.307087.153073965..103536313036...77595353266488...58237100230743229

.1452.838936.888863183.1496475492375.2984253200734849.6049936223396297740

Examples

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

Links

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

Crossrefs

Column 1 is A000574(n+1).

Formula

Empirical for column k:

k=1: a(n) = (1/120)*n^5 + (1/8)*n^4 + (5/24)*n^3 - (1/8)*n^2 - (13/60)*n

k=2: [polynomial of degree 15]

k=3: [polynomial of degree 43]

k=4: [polynomial of degree 125]