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A229774
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T(n,k)=Number of n X n 0..k arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order
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9
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..62
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FORMULA
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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]
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EXAMPLE
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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
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CROSSREFS
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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
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Sep 29 2013
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STATUS
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approved
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