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

1,1

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A000984

Row 1 is A000027(n+1)

Row 2 is A071239(n+1)

Sequence in context: A126063 A214352 A248090 * A137524 A282507 A156055

Adjacent sequences: A229771 A229772 A229773 * A229775 A229776 A229777

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 29 2013

Status

approved