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A252930
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T(n,k) = Number of n X k nonnegative integer arrays with upper left 0 and lower right n+k-6 and value increasing by 0 or 1 with every step right or down.
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10
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 5, 19, 33, 33, 19, 5, 15, 120, 413, 615, 413, 120, 15, 35, 483, 2859, 6997, 6997, 2859, 483, 35, 70, 1500, 13976, 53950, 84910, 53950, 13976, 1500, 70, 126, 3923, 54199, 315198, 762227, 762227, 315198, 54199, 3923, 126, 210
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OFFSET
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1,16
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COMMENTS
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Table starts
...0....0......0........0.........1...........5...........15............35
...0....0......0........1........19.........120..........483..........1500
...0....0......1.......33.......413........2859........13976.........54199
...0....1.....33......615......6997.......53950.......315198.......1499394
...1...19....413.....6997.....84910......762227......5385305......31454256
...5..120...2859....53950....762227.....8241540.....71297441.....512868867
..15..483..13976...315198...5385305....71297441....759337545....6725497344
..35.1500..54199..1499394..31454256...512868867...6725497344...73117894428
..70.3923.177848..6083808.157376166..3160111147..50869309436..675539536773
.126.9069.513905.21733215.692347393.17063990547.335549742230.5411459549576
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = (1/24)*n^4 - (5/12)*n^3 + (35/24)*n^2 - (25/12)*n + 1.
k=2: [polynomial of degree 8]
k=3: [polynomial of degree 12]
k=4: [polynomial of degree 16]
k=5: [polynomial of degree 20]
k=6: [polynomial of degree 24]
k=7: [polynomial of degree 28]
Empirical: with "n+k-3" instead of "n+k-6" T(n,k) = binomial(n+k,k) - 2.
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EXAMPLE
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Some solutions for n=4, k=4:
..0..1..1..1....0..0..0..0....0..0..0..0....0..1..1..2....0..0..0..1
..1..1..1..1....1..1..1..1....0..0..0..1....1..1..2..2....0..1..1..2
..1..1..2..2....1..1..1..1....1..1..1..1....1..1..2..2....0..1..1..2
..1..2..2..2....1..1..1..2....1..2..2..2....1..2..2..2....1..2..2..2
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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