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A250632
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T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction
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16
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36, 154, 125, 585, 654, 380, 2183, 2969, 2347, 1072, 7924, 12360, 12151, 7342, 2856, 28456, 49310, 56232, 43185, 20743, 7307, 101308, 190213, 241742, 218680, 134878, 53847, 18131, 358990, 720347, 994030, 1014946, 747039, 381834, 130848, 43966
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OFFSET
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1,1
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COMMENTS
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Table starts
.....36.....154......585.....2183......7924......28456......101308.......358990
....125.....654.....2969....12360.....49310.....190213......720347......2690076
....380....2347....12151....56232....241742.....994030.....3951204.....15376595
...1072....7342....43185...218680...1014946....4416061....18465586.....74732823
...2856...20743...134878...747039...3719562...17202711....75537881....319253573
...7307...53847...381834..2290189..12291286...60472234...280151655...1237636447
..18131..130848...994281..6421141..37072806..195029867...955747123...4434468137
..43966..300960..2419996.16675794.103697021..584383121..3044656152..14889326715
.104755..662000..5560799.40596068.271291108.1641320797..9115002626..47182771424
.246252.1402495.12176364.93379730.669808747.4350649060.25819633391.141867614165
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LINKS
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FORMULA
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Empirical for column k:
k=1: [linear recurrence of order 9]
k=2: [order 14]
k=3: [order 20]
k=4: [order 21] for n>24; also a degree 14 polynomial plus a degree 5 quasipolynomial with period 2
k=5: [order 22] for n>29; also a degree 14 polynomial plus a degree 6 quasipolynomial with period 2
k=6: [order 25] for n>36; also a degree 16 polynomial plus a degree 7 quasipolynomial with period 2
k=7: [order 28] for n>43; also a degree 18 polynomial plus a degree 8 quasipolynomial with period 2
Empirical for row n:
n=1: [linear recurrence of order 8]
n=2: [order 13] for n>16
n=3: [order 26] for n>29
n=4: [order 33] for n>37
n=5: [order 49] for n>54
n=6: [order 57] for n>63
n=7: [order 79] for n>86
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EXAMPLE
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Some solutions for n=3 k=4
..0..0..0..0..0....0..0..0..0..2....0..0..1..1..1....0..0..0..0..2
..0..0..0..0..0....0..0..1..1..2....0..1..1..1..2....0..0..0..0..2
..0..0..0..0..1....0..1..1..2..1....0..2..1..2..2....0..1..0..0..2
..0..2..2..1..0....2..0..2..1..2....2..1..2..2..2....2..0..1..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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