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

1,2

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A000574(n+1).

Sequence in context: A068415 A127539 A342837 * A231908 A226610 A332840

Adjacent sequences: A278624 A278625 A278626 * A278628 A278629 A278630

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 24 2016

Status

approved