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A250819
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Number of (7+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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41112, 131455, 315561, 641571, 1167796, 1962717, 3104985, 4683421, 6797016, 9554931, 13076497, 17491215, 22938756, 29568961, 37541841, 47027577, 58206520, 71269191, 86416281, 103858651, 123817332, 146523525, 172218601, 201154101
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OFFSET
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1,1
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..126
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FORMULA
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Empirical: a(n) = (1695/4)*n^4 + 3786*n^3 + (54287/4)*n^2 + (33539/2)*n + 6561.
Conjectures from Colin Barker, Nov 21 2018: (Start)
G.f.: x*(41112 - 74105*x + 69406*x^2 - 32804*x^3 + 6561*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=2:
..1..0..0....1..0..0....1..1..2....2..1..0....1..1..1....0..0..0....2..2..0
..0..0..0....0..0..0....0..0..1....0..0..0....1..1..1....0..0..0....0..0..0
..1..1..1....1..1..2....1..1..2....0..0..0....0..0..0....1..1..1....2..2..2
..1..1..1....0..0..1....0..0..1....0..1..1....0..0..0....2..2..2....2..2..2
..0..0..0....1..1..2....0..0..1....0..1..2....2..2..2....2..2..2....2..2..2
..0..0..0....0..0..1....1..1..2....0..1..2....2..2..2....1..1..1....0..0..0
..1..2..2....0..0..1....1..1..2....0..1..2....0..0..0....0..0..0....0..0..0
..0..2..2....0..0..2....0..1..2....0..1..2....1..1..1....0..0..1....0..1..1
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CROSSREFS
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Row 7 of A250812.
Sequence in context: A237395 A252121 A252118 * A234546 A344456 A257422
Adjacent sequences: A250816 A250817 A250818 * A250820 A250821 A250822
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Nov 27 2014
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STATUS
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approved
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