A229774 T(n,k)=Number of n X n 0..k arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order.

2, 3, 6, 4, 22, 20, 5, 60, 322, 70, 6, 135, 3232, 12958, 252, 7, 266, 21331, 1058494, 2179956, 924, 8, 476, 103222, 35452250, 3062815568, 1976588468, 3432, 9, 792, 397460, 637396928, 843211336888, 90462380211862, 10811999412826, 12870, 10

Offset: 1

Author

R. H. Hardin, Sep 29 2013

Keywords

• nonn
• tabl

Comments

Table starts

...2..........3..............4..................5.....................6

...6.........22.............60................135...................266

..20........322...........3232..............21331................103222

..70......12958........1058494...........35452250.............637396928

.252....2179956.....3062815568.......843211336888........81937334158292

.924.1976588468.90462380211862.322942973130396495.245200063296427870294

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..62

Crossrefs

Column 1 is A000984

Row 1 is A000027(n+1)

Row 2 is A071239(n+1)

Formula

Empirical for row n:

n=1: a(n) = n + 1

n=2: a(n) = (1/6)*n^4 + (5/6)*n^3 + (11/6)*n^2 + (13/6)*n + 1

n=3: [polynomial of degree 9]

n=4: [polynomial of degree 16]