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A203293
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Number of arrays of 6 nondecreasing integers in -n..n with sum zero and equal numbers greater than zero and less than zero.
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1
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4, 10, 28, 69, 154, 310, 580, 1013, 1680, 2662, 4064, 6005, 8634, 12114, 16644, 22441, 29760, 38878, 50116, 63817, 80374, 100206, 123784, 151609, 184240, 222266, 266340, 317149, 375446, 442022, 517740, 603501, 700284, 809110, 931080, 1067341, 1219126
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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) -a(n-2) -4*a(n-3) +2*a(n-4) +2*a(n-5) +2*a(n-6) -4*a(n-7) -a(n-8) +3*a(n-9) -a(n-10).
Empirical g.f.: x*(4 - 2*x + 2*x^2 + 11*x^3 + 7*x^4 + x^5 - 4*x^6 + x^7 + 3*x^8 - x^9) / ((1 - x)^6*(1 + x)^2*(1 + x + x^2)). - Colin Barker, Jun 04 2018
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EXAMPLE
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Some solutions for n=3:
.-2...-2...-2...-3...-3...-1...-3...-3....0...-2...-1...-3...-2...-3...-3...-3
..0...-2...-2...-2...-1...-1....0...-3....0...-2...-1...-2...-2...-2...-1...-1
..0....0...-1....0....0...-1....0...-1....0....0....0...-2...-2...-1....0...-1
..0....0....1....0....0....1....0....2....0....0....0....2....2....2....0....1
..0....1....2....2....2....1....0....2....0....2....1....2....2....2....1....1
..2....3....2....3....2....1....3....3....0....2....1....3....2....2....3....3
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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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