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A241508
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Number of partitions of n such that (number parts having multiplicity 1) is a part and (number of 1s) is not a part.
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5
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0, 0, 0, 0, 0, 3, 3, 5, 5, 10, 10, 17, 21, 34, 36, 60, 70, 97, 119, 165, 199, 275, 324, 424, 526, 685, 806, 1057, 1263, 1586, 1918, 2409, 2868, 3584, 4266, 5239, 6282, 7679, 9068, 11086, 13157, 15809, 18776, 22536, 26558, 31833, 37429, 44465, 52373, 62037
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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: 42, 411, 2111.
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MATHEMATICA
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z = 52; f[n_] := f[n] = IntegerPartitions[n]; u[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] == 1 &]]];
Table[Count[f[n], p_ /; MemberQ[p, u[p]] && MemberQ[p, Count[p, 1]]], {n, 0, z}] (* A241506 *)
Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && MemberQ[p, Count[p, 1]] ], {n, 0, z}] (* A241507 *)
Table[Count[f[n], p_ /; MemberQ[p, u[p]] && ! MemberQ[p, Count[p, 1]] ], {n, 0, z}] (* A241508 *)
Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && ! MemberQ[p, Count[p, 1]] ], {n, 0, z}] (* A241509 *)
Table[Count[f[n], p_ /; MemberQ[p, u[p]] || MemberQ[p, Count[p, 1]] ], {n, 0, z}] (* A241510 *)
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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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