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A201814
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Number of arrays of 6 integers in -n..n with sum zero and equal numbers of elements greater than zero and less than zero.
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1
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141, 1001, 4621, 15681, 42821, 99961, 207621, 394241, 697501, 1165641, 1858781, 2850241, 4227861, 6095321, 8573461, 11801601, 15938861, 21165481, 27684141, 35721281, 45528421, 57383481, 71592101, 88488961, 108439101, 131839241
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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) = 11*n^5 + 65*n^3 + 64*n + 1.
G.f.: x*(141 + 155*x + 730*x^2 + 150*x^3 + 145*x^4 - x^5) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
(End)
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EXAMPLE
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Some solutions for n=6:
..6....4....2...-5...-6....6....2...-2...-4...-4...-4....0....4...-4....5...-4
.-5....1....6...-1....2....5...-4...-4...-1....1...-3....5...-1....1...-3...-1
.-4...-4...-5....3....5....1...-2....0....3...-1....4...-4....3...-4...-5....4
..1...-2...-4....5...-1...-5....2....2...-6....6....1....0...-4...-1....5....1
.-1....4...-3...-4...-6...-5...-1....0....6....1...-3...-2...-6....2....2...-4
..3...-3....4....2....6...-2....3....4....2...-3....5....1....4....6...-4....4
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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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