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A201812
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Number of arrays of 4 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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19, 61, 151, 313, 571, 949, 1471, 2161, 3043, 4141, 5479, 7081, 8971, 11173, 13711, 16609, 19891, 23581, 27703, 32281, 37339, 42901, 48991, 55633, 62851, 70669, 79111, 88201, 97963, 108421, 119599, 131521, 144211, 157693, 171991, 187129, 203131
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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) = 4*n^3 + 14*n + 1.
G.f.: x*(19 - 15*x + 21*x^2 - x^3) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)
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EXAMPLE
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Some solutions for n=21:
-6 15 -3 -8 -13 1 13 16 15 -15 3 -21 -6 8 -11 1
9 -12 8 9 9 21 -2 -18 13 9 -7 12 3 20 -18 18
4 -18 16 -17 -13 -14 -13 9 -20 21 -16 19 -11 -7 21 -15
-7 15 -21 16 17 -8 2 -7 -8 -15 20 -10 14 -21 8 -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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