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A229774 T(n,k)=Number of n X n 0..k arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order 9
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 5 00:21 EST 2021. Contains 349530 sequences. (Running on oeis4.)