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A241410 Number of partitions of n such that the number of parts having multiplicity >1 is not a part and the number of distinct parts is a part. 5
0, 1, 0, 1, 0, 1, 2, 2, 4, 5, 7, 8, 12, 17, 22, 29, 33, 49, 59, 77, 97, 123, 153, 199, 234, 306, 375, 460, 557, 708, 845, 1048, 1266, 1548, 1852, 2282, 2698, 3303, 3919, 4732, 5634, 6786, 7991, 9598, 11343, 13502, 15897, 18912, 22180, 26298, 30775, 36259 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,7
COMMENTS
As used here, the term "distinct parts" includes each number, once, that occurs more than once; e.g., the distinct parts of the partition {4,3,3,1,1,1} are 4, 3, 1.
LINKS
EXAMPLE
a(6) counts these 2 partitions: 42, 321.
MATHEMATICA
z = 30; f[n_] := f[n] = IntegerPartitions[n]; e[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] > 1 &]]]; d[p_] := Length[DeleteDuplicates[p]];
Table[Count[f[n], p_ /; MemberQ[p, e[p]]], {n, 0, z}] (* A241408 *)
Table[Count[f[n], p_ /; MemberQ[p, e[p]] && MemberQ[p, d[p]]], {n, 0, z}] (* A241409 *)
Table[Count[f[n], p_ /; ! MemberQ[p, e[p]] && MemberQ[p, d[p]] ], {n, 0, z}] (* A241410 *)
Table[Count[f[n], p_ /; MemberQ[p, e[p]] && ! MemberQ[p, d[p]] ], {n, 0, z}] (* A241411 *)
Table[Count[f[n], p_ /; ! MemberQ[p, e[p]] && ! MemberQ[p, d[p]] ], {n, 0, z}] (* A241412 *)
CROSSREFS
Sequence in context: A338202 A348552 A058678 * A324753 A283106 A030769
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 22 2014
STATUS
approved

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Last modified March 4 12:21 EST 2024. Contains 370532 sequences. (Running on oeis4.)