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A188272
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Number of nondecreasing strings of numbers x(i=1..n) in -4..4 with sum x(i)^3 equal to 0
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1
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1, 5, 5, 15, 15, 37, 41, 84, 106, 186, 256, 400, 570, 834, 1184, 1663, 2305, 3149, 4241, 5669, 7455, 9771, 12607, 16216, 20592, 26014, 32578, 40526, 50112, 61530, 75192, 91301, 110337, 132665, 158727, 189151, 224311, 265107, 311919, 365808, 427366
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = [y^0] [x^n] Product_{j=-4..4} 1/(1-x*y^(j^3)). - Robert Israel, Feb 06 2019
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EXAMPLE
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Some solutions for n=8 k=4
.-2...-3...-4...-4...-3...-3...-4...-3...-1...-3...-4...-4...-4...-1...-4...-3
.-2...-2...-4...-4...-3...-2...-4...-2...-1...-2...-4...-3...-3...-1...-2...-3
.-1....0...-3....1...-3...-2...-3...-2...-1...-2...-3...-1...-3....0...-1...-2
..0....0...-3....1...-2....0....0...-2....0...-1...-1...-1...-1....0...-1...-1
..0....0....3....2...-1....0....0....2....0....1....1....1....1....0....1....1
..1....0....3....3...-1....2....3....2....1....2....3....1....3....0....1....2
..2....2....4....3....3....2....4....2....1....2....4....3....3....1....2....3
..2....3....4....4....4....3....4....3....1....3....4....4....4....1....4....3
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MAPLE
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P:= 1/mul(1-x*y^(j^3), j=-4..4):
S:= series(P, x, 101):
seq(coeff(coeff(S, x, n), y, 0), n=1..100); # Robert Israel, Feb 06 2019
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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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