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A266464
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Number of n X 2 binary arrays with rows and columns lexicographically nondecreasing and column sums nonincreasing.
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2
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1, 2, 4, 7, 12, 19, 29, 42, 59, 80, 106, 137, 174, 217, 267, 324, 389, 462, 544, 635, 736, 847, 969, 1102, 1247, 1404, 1574, 1757, 1954, 2165, 2391, 2632, 2889, 3162, 3452, 3759, 4084, 4427, 4789, 5170, 5571, 5992, 6434, 6897, 7382, 7889, 8419, 8972, 9549, 10150
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) -a(n-5).
G.f.: (x^3-x+1)/((x+1)*(x-1)^4).
a(n) = (2*n^3 + 3*n^2 + 22*n + 24) / 24 for n even.
a(n) = (2*n^3 + 3*n^2 + 22*n + 21) / 24 for n odd.
(End)
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EXAMPLE
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Some solutions for n=4:
..0..0....0..0....0..1....0..0....0..1....0..0....1..1....0..1....0..0....0..1
..0..0....0..0....0..1....1..1....1..0....0..0....1..1....1..0....0..0....1..0
..0..1....0..0....1..0....1..1....1..1....1..1....1..1....1..0....0..0....1..0
..1..0....1..1....1..0....1..1....1..1....1..1....1..1....1..1....0..0....1..0
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MAPLE
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a:= proc(n) option remember;
`if`(n<0, 0, 1+a(n-1)+floor(n^2/4))
end:
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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