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A250817
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Number of (5+1) X (n+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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1
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4356, 13735, 32745, 66291, 120304, 201741, 318585, 479845, 695556, 976779, 1335601, 1785135, 2339520, 3013921, 3824529, 4788561, 5924260, 7250895, 8788761, 10559179, 12584496, 14888085, 17494345, 20428701, 23717604, 27388531, 31469985
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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) = (171/4)*n^4 + 390*n^3 + (5627/4)*n^2 + (3575/2)*n + 729.
G.f.: x*(4356 - 8045*x + 7630*x^2 - 3644*x^3 + 729*x^4) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)
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EXAMPLE
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Some solutions for n=4:
..1..1..1..2..2....0..0..0..0..0....2..2..2..0..1....2..0..0..0..0
..1..1..1..2..2....1..1..1..1..1....0..0..0..0..1....0..0..0..0..0
..1..1..1..2..2....1..1..1..1..1....0..0..0..0..1....1..1..1..1..1
..0..0..0..1..1....0..0..0..0..0....1..1..1..1..2....0..0..0..0..0
..0..0..1..2..2....0..0..2..2..2....1..1..1..1..2....0..0..0..0..0
..0..0..1..2..2....0..0..2..2..2....0..0..0..0..1....0..1..1..1..2
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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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