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A201347
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Number of n X 2 0..1 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor.
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1
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2, 4, 8, 14, 23, 36, 54, 78, 109, 148, 196, 254, 323, 404, 498, 606, 729, 868, 1024, 1198, 1391, 1604, 1838, 2094, 2373, 2676, 3004, 3358, 3739, 4148, 4586, 5054, 5553, 6084, 6648, 7246, 7879, 8548, 9254, 9998, 10781, 11604, 12468, 13374, 14323, 15316, 16354
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = (1/6)*n^3 - (1/2)*n^2 + (10/3)*n - 2 for n>1.
G.f.: x*(2 - 4*x + 4*x^2 - 2*x^3 + x^4) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5.
(End)
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EXAMPLE
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Some solutions for n=10:
..0..0....0..0....0..0....0..0....0..1....0..1....0..0....0..0....0..0....0..0
..0..0....0..0....0..0....0..0....0..1....0..1....0..0....0..1....0..1....0..0
..0..1....0..0....0..0....0..0....1..0....0..1....0..0....0..1....0..1....0..0
..0..1....0..0....1..1....0..1....1..0....0..1....0..0....0..1....0..1....0..0
..0..1....0..0....1..1....0..1....1..0....0..1....0..0....1..0....1..0....0..0
..0..1....0..0....1..1....0..1....1..0....1..0....0..0....1..0....1..0....0..1
..0..1....0..0....1..1....1..1....1..0....1..0....0..1....1..0....1..0....0..1
..0..1....0..0....1..1....1..1....1..0....1..0....0..1....1..1....1..0....0..1
..1..0....0..1....1..1....1..1....1..1....1..0....0..1....1..1....1..0....1..0
..1..0....1..1....1..1....1..1....1..1....1..0....1..1....1..1....1..1....1..0
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MATHEMATICA
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Rest@ CoefficientList[Series[x (2 - 4 x + 4 x^2 - 2 x^3 + x^4)/(1 - x)^4, {x, 0, 47}], x] (* Michael De Vlieger, Mar 27 2020 *)
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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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