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A241274
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Number of partitions p of n such that (number of numbers in p that have multiplicity 1) = (number of numbers in p having multiplicity > 1).
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6
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1, 0, 0, 0, 1, 3, 3, 7, 7, 10, 12, 16, 14, 23, 25, 33, 41, 59, 72, 101, 126, 171, 216, 280, 344, 436, 535, 666, 788, 970, 1153, 1394, 1649, 1996, 2336, 2796, 3326, 3965, 4689, 5627, 6629, 7926, 9404, 11192, 13273, 15777, 18637, 22057, 26067, 30672, 36122
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OFFSET
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0,6
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LINKS
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FORMULA
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EXAMPLE
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a(6) counts these 3 partitions: 411, 3111, 21111.
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MATHEMATICA
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z = 30; u[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] == 1 &]]]; e[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] > 1 &]]]; Table[Count[IntegerPartitions[n], p_ /; u[p] == e[p]], {n, 0, z}]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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