A250899 revision #6
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A250899
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Number of (1+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.
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1
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37, 127, 403, 1229, 3673, 10875, 32095, 94729, 280069, 829943, 2465227, 7338309, 21883825, 65356531, 195414199, 584800769, 1751256541, 5246953839, 15726181411, 47147086909, 141374151817, 423979849067, 1271637557263, 3814275137529
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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) = 9*a(n-1) - 31*a(n-2) + 51*a(n-3) - 40*a(n-4) + 12*a(n-5).
G.f.: x*(37 - 206*x + 407*x^2 - 348*x^3 + 108*x^4) / ((1 - x)^2*(1 - 2*x)^2*(1 - 3*x)).
a(n) = (7 - 2^(4+n) + 3^(3+n) + (2+2^(3+n))*n) / 2.
(End)
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EXAMPLE
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Some solutions for n=4:
..1..1..1..0..0....0..2..2..1..0....2..1..1..2..1....2..2..1..2..0
..2..2..2..1..1....0..2..2..1..2....2..1..1..2..1....2..2..1..2..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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proposed
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