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A250815
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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 min(x(i,j),x(i-1,j)) in the j direction.
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1
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432, 1315, 3081, 6171, 11116, 18537, 29145, 43741, 63216, 88551, 120817, 161175, 210876, 271261, 343761, 429897, 531280, 649611, 786681, 944371, 1124652, 1329585, 1561321, 1822101, 2114256, 2440207, 2802465, 3203631, 3646396, 4133541, 4667937
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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) = (15/4)*n^4 + 36*n^3 + (527/4)*n^2 + (359/2)*n + 81.
G.f.: x*(432 - 845*x + 826*x^2 - 404*x^3 + 81*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..2..2..2..2....2..1..1..2..2....2..2..1..0..0....1..1..1..1..1
..0..1..1..1..1....1..1..1..2..2....0..0..0..0..0....1..1..1..2..2
..1..2..2..2..2....1..1..1..2..2....0..0..0..0..1....1..1..1..2..2
..1..2..2..2..2....1..1..1..2..2....0..0..1..1..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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