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A240674
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Number of partitions p of n that are disjoint from their conjugate.
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2
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0, 2, 2, 2, 2, 4, 4, 8, 10, 10, 14, 18, 18, 26, 30, 36, 44, 60, 64, 82, 96, 114, 130, 164, 176, 222, 248, 296, 338, 406, 450, 550, 620, 726, 816, 968, 1074, 1270, 1418, 1648, 1836, 2150, 2382, 2758, 3080, 3534, 3942, 4538, 5034, 5778, 6416, 7312, 8136, 9258
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OFFSET
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1,2
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COMMENTS
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First column of the array at A240181.
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LINKS
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FORMULA
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EXAMPLE
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a(6) counts these 4 partitions: 6, 33, 222, 111111, of which the respective conjugates are 111111, 222, 33, 6.
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MATHEMATICA
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z = 30; p[n_, k_] := p[n, k] = IntegerPartitions[n][[k]]; c[p_] := c[p] = Table[Count[#, _?(# >= i &)], {i, First[#]}] &[p]; b[n_] := b[n] = Table[Intersection[p[n, k], c[p[n, k]]], {k, 1, PartitionsP[n]}]; Table[Count[Map[Length, b[n]], 0], {n, 1, z}] (* this sequence *)
Table[Count[Map[Length, b[n]], 1], {n, 1, z}] (* A240675 *)
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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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EXTENSIONS
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STATUS
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approved
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