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A361802
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Irregular triangle read by rows where T(n,k) is the number of k-subsets of {-n+1,...,n} with sum 0, for k = 1,...,2n-1.
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0
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1, 1, 1, 1, 1, 2, 3, 2, 1, 1, 3, 6, 7, 5, 2, 1, 1, 4, 10, 16, 18, 14, 8, 3, 1, 1, 5, 15, 31, 46, 51, 43, 27, 12, 3, 1, 1, 6, 21, 53, 98, 139, 155, 134, 88, 43, 16, 4, 1, 1, 7, 28, 83, 184, 319, 441, 486, 424, 293, 161, 68, 21, 4, 1
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OFFSET
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1,6
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COMMENTS
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Also the number of k-subsets of {1,...,2n} with mean n.
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LINKS
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EXAMPLE
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Triangle begins:
1
1 1 1
1 2 3 2 1
1 3 6 7 5 2 1
1 4 10 16 18 14 8 3 1
1 5 15 31 46 51 43 27 12 3 1
1 6 21 53 98 139 155 134 88 43 16 4 1
1 7 28 83 184 319 441 486 424 293 161 68 21 4 1
Row n = 3 counts the following subsets:
{0} {-1,1} {-1,0,1} {-2,-1,0,3} {-2,-1,0,1,2}
{-2,2} {-2,0,2} {-2,-1,1,2}
{-2,-1,3}
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MATHEMATICA
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Table[Length[Select[Subsets[Range[-n+1, n], {k}], Total[#]==0&]], {n, 6}, {k, 2n-1}]
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CROSSREFS
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A067538 counts partitions with integer mean.
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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