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A214353
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Number of 3 X 3 X 3 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors.
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1
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26, 169, 660, 1951, 4822, 10507, 20840, 38421, 66802, 110693, 176188, 271011, 404782, 589303, 838864, 1170569, 1604682, 2164993, 2879204, 3779335, 4902150, 6289603, 7989304, 10055005, 12547106, 15533181, 19088524, 23296715, 28250206
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = (1/36)*n^6 + (7/15)*n^5 + (25/9)*n^4 + (15/2)*n^3 + (331/36)*n^2 + (151/30)*n + 1.
G.f.: x*(26 - 13*x + 23*x^2 - 30*x^3 + 20*x^4 - 7*x^5 + x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)
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EXAMPLE
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Some solutions for n=3:
....1......1......2......1......2......1......3......2......3......2......0
...2.0....1.1....2.1....1.1....2.2....1.2....3.1....0.3....0.3....1.3....1.0
..3.2.0..0.3.1..3.1.3..0.3.0..2.2.0..2.1.2..3.1.0..0.3.2..0.1.3..1.2.3..3.1.0
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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