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A225311
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Number of 4 X n -1,1 arrays such that the sum over i=1..4,j=1..n of i*x(i,j) is zero and rows are nondecreasing (ways to put n thrusters pointing east or west at each of 4 positions 1..n distance from the hinge of a south-pointing gate without turning the gate).
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1
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2, 7, 16, 31, 52, 83, 122, 175, 238, 317, 410, 523, 650, 801, 970, 1165, 1380, 1625, 1892, 2193, 2518, 2879, 3268, 3697, 4154, 4655, 5188, 5767, 6380, 7043, 7742, 8495, 9286, 10133, 11022, 11971, 12962, 14017, 15118, 16285, 17500, 18785, 20120, 21529, 22990
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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) = a(n-1) + a(n-2) - 2*a(n-5) + a(n-8) + a(n-9) - a(n-10).
Empirical g.f.: x*(2 + 5*x + 7*x^2 + 8*x^3 + 5*x^4 + 4*x^5 + x^6 + 2*x^7 + x^8 - x^9) / ((1 - x)^4*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Sep 05 2018
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EXAMPLE
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Some solutions for n=4:
.-1.-1..1..1...-1.-1..1..1...-1.-1..1..1....1..1..1..1...-1.-1..1..1
.-1.-1.-1..1...-1..1..1..1...-1.-1.-1..1...-1..1..1..1...-1.-1..1..1
..1..1..1..1....1..1..1..1...-1.-1.-1.-1...-1.-1..1..1...-1.-1..1..1
.-1.-1.-1..1...-1.-1.-1.-1....1..1..1..1...-1.-1.-1..1...-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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