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 A241442 Number of partitions of n such that the number of parts having multiplicity 1 is a part and the number of distinct parts is a part. 5
 0, 1, 0, 1, 1, 3, 3, 4, 5, 8, 9, 12, 17, 25, 30, 43, 52, 73, 93, 119, 147, 191, 238, 303, 370, 473, 573, 721, 873, 1089, 1326, 1640, 1954, 2438, 2900, 3556, 4240, 5181, 6140, 7452, 8851, 10626, 12600, 15090, 17812, 21248, 25063, 29686, 34969, 41344, 48465 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS FORMULA a(n) + A241443(n) + A241444(n) = A241446(n) for n >= 0. EXAMPLE a(6) counts these 3 partitions:  42, 321, 21111. MATHEMATICA z = 30; f[n_] := f[n] = IntegerPartitions[n]; u[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] == 1 &]]]; d[p_] := Length[DeleteDuplicates[p]]; Table[Count[f[n], p_ /; MemberQ[p, u[p]] && MemberQ[p, d[p]]], {n, 0, z}]  (* A241442 *) Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && MemberQ[p, d[p]] ], {n, 0,  z}] (* A241443 *) Table[Count[f[n], p_ /; MemberQ[p, u[p]] && ! MemberQ[p, d[p]] ], {n, 0, z}] (* A241444 *) Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && ! MemberQ[p, d[p]] ], {n, 0, z}] (* A241445 *) Table[Count[f[n], p_ /; MemberQ[p, u[p]] || MemberQ[p, d[p]] ], {n, 0, z}] (* A241446 *) CROSSREFS Cf. A241443, A241444, A241445, A241446. Sequence in context: A100091 A239483 A104806 * A043551 A162888 A151759 Adjacent sequences:  A241439 A241440 A241441 * A241443 A241444 A241445 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 23 2014 STATUS approved

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Last modified September 24 11:38 EDT 2020. Contains 337318 sequences. (Running on oeis4.)