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A241416
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Number of partitions p of n such that the number of numbers having multiplicity 1 in p is a part and the number of numbers having multiplicity > 1 is not a part.
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7
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0, 1, 0, 1, 0, 1, 2, 1, 2, 3, 4, 4, 8, 14, 16, 28, 33, 47, 61, 83, 98, 131, 157, 201, 248, 312, 379, 480, 589, 730, 903, 1136, 1373, 1725, 2095, 2593, 3129, 3870, 4625, 5677, 6774, 8215, 9759, 11813, 13896, 16738, 19675, 23515, 27580, 32846, 38349, 45528
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OFFSET
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0,7
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LINKS
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FORMULA
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EXAMPLE
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a(6) counts these 2 partitions: 42, 321.
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MATHEMATICA
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z = 30; f[n_] := f[n] = IntegerPartitions[n]; u[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] == &]]]; e[q_] := Length[DeleteDuplicates[Select[q, Count[q, #] > 1 &]]]
Table[Count[f[n], p_ /; MemberQ[p, u[p]]], {n, 0, z}] (* A241413 *)
Table[Count[f[n], p_ /; MemberQ[p, u[p]] && MemberQ[p, e[p]]], {n, 0, z}] (* A241414 *)
Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && MemberQ[p, e[p]] ], {n, 0, z}] (* A241415 *)
Table[Count[f[n], p_ /; MemberQ[p, u[p]] && ! MemberQ[p, e[p]] ], {n, 0, z}] (* A241416 *)
Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && ! MemberQ[p, e[p]] ], {n, 0, z}] (* A241417 *)
Table[Count[f[n], p_ /; MemberQ[p, u[p]] || MemberQ[p, e[p]] ], {n, 0, z}] (* A239737 *)
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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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