A278778 - OEIS

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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,5

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

LINKS

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

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]

EXAMPLE

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

CROSSREFS

Column 1 is A000389(n+1).

Sequence in context: A267164 A158234 A270882 * A356817 A285931 A069845

Adjacent sequences: A278775 A278776 A278777 * A278779 A278780 A278781

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Nov 28 2016

STATUS

approved