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A202027
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Number of n X 2 zero-sum -1..1 arrays with rows and columns lexicographically nondecreasing.
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1
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2, 7, 21, 56, 130, 281, 555, 1034, 1827, 3090, 5028, 7929, 12143, 18144, 26512, 37981, 53440, 74001, 100965, 135932, 180770, 237705, 309317, 398656, 509191, 644982, 810632, 1011433, 1253353, 1543214, 1888620, 2298205, 2781564, 3349469, 4013843
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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) = 3*a(n-1) -6*a(n-3) +6*a(n-5) +7*a(n-6) -9*a(n-7) -9*a(n-8) +7*a(n-9) +6*a(n-10) -6*a(n-12) +3*a(n-14) -a(n-15).
Empirical g.f.: x*(2 + x + 5*x^3 + 4*x^4 + 5*x^5 - 8*x^6 - 8*x^7 + 9*x^8 + 5*x^9 - 2*x^10 - 5*x^11 + 3*x^13 - x^14) / ((1 - x)^8*(1 + x)^3*(1 + x + x^2)^2). - Colin Barker, May 25 2018
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EXAMPLE
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Some solutions for n=10:
.-1.-1...-1.-1...-1.-1...-1..0...-1.-1...-1.-1...-1.-1...-1.-1...-1.-1...-1..0
.-1..1...-1.-1...-1.-1...-1..0...-1..1...-1.-1...-1..1...-1.-1...-1.-1...-1..0
.-1..1...-1.-1...-1.-1....0.-1....0..0...-1.-1...-1..1...-1.-1...-1..1...-1..0
.-1..1...-1..1....0..0....0..0....0..0...-1..1...-1..1....0..0....0..0....0..1
..0.-1....0..1....0..1....0..0....0..1....0..0...-1..1....0..1....0..0....1.-1
..0..1....0..1....1.-1....0..0....0..1....0..1...-1..1....0..1....1.-1....1.-1
..0..1....0..1....1..0....0..0....1.-1....0..1....0..0....0..1....1.-1....1.-1
..1.-1....0..1....1..0....1.-1....1.-1....0..1....0..0....0..1....1..0....1.-1
..1.-1....1.-1....1..0....1..0....1.-1....0..1....0..0....0..1....1..0....1.-1
..1..0....1..1....1..1....1..1....1.-1....1..1....1..1....1..0....1..1....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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