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A199533
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Number of -n..n arrays x(0..5) of 6 elements with zero sum and no two consecutive zero elements.
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1
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80, 1414, 8342, 30484, 84852, 197962, 407946, 766664, 1341816, 2219054, 3504094, 5324828, 7833436, 11208498, 15657106, 21416976, 28758560, 37987158, 49445030, 63513508, 80615108, 101215642, 125826330, 155005912, 189362760, 229556990
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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) = (88/5)*n^5 + 44*n^4 + (58/3)*n^3 - 3*n^2 + (31/15)*n.
G.f.: 2*x*(40 + 467*x + 529*x^2 + 21*x^3 - x^4) / (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=5:
..1....5...-4....0....5...-3...-1...-3....5....5...-5....0...-3....3....3....4
..3....1....2....5....5...-1....2...-4....4...-3...-2...-3....4....3....1...-1
..3...-5...-3...-3....1...-1....5....1...-5....3....3....4...-3...-1....3....1
.-1....0....4...-2...-3...-4...-3...-2....0....0....5....0...-1...-5....0....0
.-2...-3....4...-4...-3....4...-2....3...-5...-5....2...-3...-1....2...-2...-2
.-4....2...-3....4...-5....5...-1....5....1....0...-3....2....4...-2...-5...-2
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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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