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A250758
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Number of (3+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.
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1
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332, 756, 1353, 2123, 3066, 4182, 5471, 6933, 8568, 10376, 12357, 14511, 16838, 19338, 22011, 24857, 27876, 31068, 34433, 37971, 41682, 45566, 49623, 53853, 58256, 62832, 67581, 72503, 77598, 82866, 88307, 93921, 99708, 105668, 111801, 118107
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OFFSET
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1,1
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LINKS
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FORMULA
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Empirical: a(n) = (173/2)*n^2 + (329/2)*n + 81.
G.f.: x*(332 - 240*x + 81*x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
(End)
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EXAMPLE
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Some solutions for n=4:
..1..1..2..2..2....2..2..2..2..2....1..1..1..1..1....0..0..0..0..0
..0..0..1..1..1....0..0..0..1..1....2..2..2..2..2....0..0..0..0..0
..0..0..1..1..1....0..0..0..1..1....0..0..0..0..2....2..2..2..2..2
..0..0..1..1..1....0..0..0..1..2....0..0..0..0..2....0..0..0..1..1
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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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