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A240729
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Number of partitions p of n such that m(p) < m(c(p)), where m = minimal multiplicity of parts, and c = conjugate.
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6
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0, 1, 1, 1, 1, 3, 2, 5, 4, 8, 7, 13, 11, 19, 19, 26, 28, 44, 40, 61, 63, 89, 91, 128, 127, 181, 188, 248, 258, 350, 357, 474, 497, 641, 674, 870, 906, 1167, 1229, 1537, 1634, 2058, 2163, 2691, 2866, 3523, 3753, 4603, 4883, 5969, 6372, 7676, 8226
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OFFSET
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1,6
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LINKS
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FORMULA
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EXAMPLE
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a(7) counts these 2 partitions: 7, 52, of which the respective conjugates are 1111111, 22111.
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MATHEMATICA
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z = 30; f[n_] := f[n] = IntegerPartitions[n]; c[p_] := Table[Count[#, _?(# >= i &)], {i, First[#]}] &[p]; m[p_] := Min[Map[Length, Split[p]]];
Table[Count[f[n], p_ /; m[p] < m[c[p]]], {n, 1, z}] (* A240729 *)
Table[Count[f[n], p_ /; m[p] <= m[c[p]]], {n, 1, z}] (* A240730 *)
Table[Count[f[n], p_ /; m[p] == m[c[p]]], {n, 1, z}] (* A240731 *)
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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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