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A271034
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T(n,k)=Number of nXnXn triangular 0..k arrays with some element less than a w, nw or ne neighbor exactly once.
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12
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0, 0, 2, 0, 8, 10, 0, 20, 72, 34, 0, 40, 294, 450, 98, 0, 70, 896, 3114, 2420, 258, 0, 112, 2268, 15116, 29120, 12010, 642, 0, 168, 5040, 58036, 232432, 256020, 56754, 1538, 0, 240, 10164, 188034, 1402082, 3441072, 2173554, 259628, 3586, 0, 330, 19008, 535106
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OFFSET
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1,3
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COMMENTS
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Table starts
....0.......0.........0...........0............0..............0...............0
....2.......8........20..........40...........70............112.............168
...10......72.......294.........896.........2268...........5040...........10164
...34.....450......3114.......15116........58036.........188034..........535106
...98....2420.....29120......232432......1402082........6872424........28658242
..258...12010....256020.....3441072.....33505396......255757328......1610555756
..642...56754...2173554....50108414....804566180.....9790184488.....95420380090
.1538..259628..18060096...724727082..19525545192...386105784866...5945425725202
.3586.1160936.147976270.10461499634.479803630966.15669594394610.387907415514308
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 5*a(n-1) -8*a(n-2) +4*a(n-3)
Empirical for row n:
n=2: a(n) = (1/3)*n^3 + n^2 + (2/3)*n
n=3: [polynomial of degree 6]
n=4: [polynomial of degree 10]
n=5: [polynomial of degree 15]
n=6: [polynomial of degree 21]
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EXAMPLE
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Some solutions for n=4 k=4
.....0........0........0........1........0........1........0........0
....0.0......0.3......1.0......2.3......0.0......1.1......0.2......0.0
...1.0.0....3.3.3....3.4.4....3.4.4....0.1.3....0.1.2....0.2.2....1.1.0
..1.1.1.1..4.4.3.4..4.4.4.4..3.3.4.4..2.4.3.3..2.3.4.4..0.0.2.3..4.4.4.4
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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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