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A250880
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Number of (3+1) X (n+1) 0..3 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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2002, 6812, 16262, 31928, 55386, 88212, 131982, 188272, 258658, 344716, 448022, 570152, 712682, 877188, 1065246, 1278432, 1518322, 1786492, 2084518, 2413976, 2776442, 3173492, 3606702, 4077648, 4587906, 5139052, 5732662, 6370312, 7053578
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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) = (788/3)*n^3 + 744*n^2 + (2218/3)*n + 256.
G.f.: 2*x*(1001 - 598*x + 513*x^2 - 128*x^3) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)
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EXAMPLE
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Some solutions for n=4:
..2..3..3..3..3....3..3..3..2..2....3..3..3..3..3....0..0..0..0..0
..1..2..2..2..2....2..2..2..3..3....2..2..2..2..2....2..2..2..3..3
..0..2..2..2..2....1..1..1..3..3....1..1..1..1..2....1..1..1..3..3
..0..3..3..3..3....0..0..0..2..3....0..2..2..2..3....0..0..0..2..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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