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A229428
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T(n,k) = Number of n X k 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, rows lexicographically nondecreasing, and columns lexicographically nonincreasing.
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9
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3, 5, 5, 8, 12, 8, 12, 27, 27, 12, 17, 55, 83, 55, 17, 23, 102, 222, 222, 102, 23, 30, 175, 524, 754, 524, 175, 30, 38, 282, 1116, 2204, 2204, 1116, 282, 38, 47, 432, 2187, 5700, 7816, 5700, 2187, 432, 47, 57, 635, 4005, 13345, 24126, 24126, 13345, 4005, 635, 57
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OFFSET
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1,1
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COMMENTS
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Table starts
..3...5....8....12.....17.....23......30.......38.......47........57........68
..5..12...27....55....102....175.....282......432......635.......902......1245
..8..27...83...222....524...1116....2187.....4005.....6936.....11465.....18219
.12..55..222...754...2204...5700...13345....28794....58053....110550....200533
.17.102..524..2204...7816..24126...66503...166972...387738....842802...1731129
.23.175.1116..5700..24126..87648..281016...812352..2152643...5297329..12231874
.30.282.2187.13345..66503.281016.1037193..3420692.10260128..28379127..73192023
.38.432.4005.28794.166972.812352.3420692.12768612.43042290.132960319.380811699
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = (1/2)*n^2 + (1/2)*n + 2
k=2: a(n) = (1/24)*n^4 + (5/12)*n^3 + (11/24)*n^2 + (25/12)*n + 2, A229422
k=3: [polynomial of degree 6], A229423
k=4: [polynomial of degree 8], A229424
k=5: [polynomial of degree 10], A229425
k=6: [polynomial of degree 12], A229426
k=7: [polynomial of degree 14]
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EXAMPLE
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Some solutions for n=4 k=4
..2..2..1..0....1..1..0..0....1..1..0..0....2..1..1..1....1..0..0..0
..2..2..1..1....2..1..0..0....2..1..0..0....2..1..1..1....1..1..1..1
..2..2..1..1....2..1..1..1....2..1..1..1....2..2..2..1....2..2..1..1
..2..2..2..1....2..1..1..1....2..2..1..1....2..2..2..2....2..2..2..1
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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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