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A199534
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Number of -n..n arrays x(0..6) of 7 elements with zero sum and no two consecutive zero elements.
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1
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200, 6346, 53302, 252154, 860854, 2378412, 5662636, 12071420, 23627580, 43207238, 74751754, 123503206, 196263418, 301676536, 450535152, 656109976, 934503056, 1305024546, 1790593022, 2418159346, 3219154078, 4229958436, 5492398804
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OFFSET
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1,1
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COMMENTS
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Row 7 of A199530.
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..200
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FORMULA
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Empirical: a(n) = (5887/180)*n^6 + (5887/60)*n^5 + (620/9)*n^4 + (11/12)*n^3 + (433/180)*n^2 - (91/30)*n.
Conjectures from Colin Barker, May 16 2018: (Start)
G.f.: 2*x*(100 + 2473*x + 6540*x^2 + 2653*x^3 + 4*x^4 + 4*x^5) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)
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EXAMPLE
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Some solutions for n=5:
.-5...-5...-4...-5...-4...-5...-4...-5...-4...-5...-5...-5...-5...-4...-5...-4
..1...-3....1....3....0...-5...-4....4...-4....5...-3....0....5...-4....3....2
..1....4...-1....0....4....2....0...-5...-1....1...-1...-2....3....1...-5....2
.-1...-2....3...-1....5...-2....5....5...-2....3...-1....4...-3....4....1....0
..4...-4...-4....1...-2....5...-1....2....3...-3....5....1....0....4....5...-1
..5....5....3...-2...-1....5...-1....0....3...-5....0....4...-2....1....5....1
.-5....5....2....4...-2....0....5...-1....5....4....5...-2....2...-2...-4....0
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CROSSREFS
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Cf. A199530.
Sequence in context: A220390 A231803 A185988 * A035747 A219414 A022152
Adjacent sequences: A199531 A199532 A199533 * A199535 A199536 A199537
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Nov 07 2011
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STATUS
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approved
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