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 A241409 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. 6
 0, 0, 1, 1, 2, 3, 3, 5, 6, 9, 12, 16, 23, 26, 39, 45, 67, 78, 106, 130, 171, 207, 270, 329, 419, 516, 637, 787, 978, 1190, 1451, 1775, 2166, 2613, 3173, 3827, 4613, 5537, 6659, 7948, 9523, 11316, 13505, 16014, 19059, 22455, 26667, 31376, 37079, 43501, 51282 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 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 3 partitions:  411, 3111, 21111. 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 Cf. A241408, A241410, A241411, A241412. Sequence in context: A036803 A179492 A230580 * A018131 A121400 A238003 Adjacent sequences:  A241406 A241407 A241408 * A241410 A241411 A241412 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 22 2014 STATUS approved

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Last modified January 24 07:45 EST 2021. Contains 340398 sequences. (Running on oeis4.)