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 A241377 Number of partitions of n such that the number of parts is a part and the number of distinct parts is a part. 5
 0, 1, 0, 1, 0, 1, 2, 2, 3, 4, 5, 6, 8, 11, 12, 16, 20, 27, 31, 40, 49, 59, 72, 95, 110, 133, 164, 196, 237, 289, 351, 410, 502, 595, 704, 843, 1009, 1193, 1422, 1658, 1983, 2332, 2744, 3204, 3796, 4459, 5189, 6083, 7116, 8292, 9677, 11222, 13041, 15235 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 LINKS FORMULA a(n) + A241378(n) + A241379(n) = A241381(n) for n >= 0. EXAMPLE a(9) counts these 4 partitions:  72, 531, 432, 4311. MATHEMATICA z = 70; f[n_] := f[n] = IntegerPartitions[n]; d[p_] := [p] = Length[DeleteDuplicates[p]]; Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && MemberQ[p, d[p]]], {n, 0, z}]  (* A241377 *) Table[Count[f[n], p_ /; ! MemberQ[p, Length[p]] && MemberQ[p, d[p]]], {n, 0, z}]  (* A241378 *) Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && ! MemberQ[p, d[p]]], {n, 0, z}]  (* A241379 *) Table[Count[f[n], p_ /; ! MemberQ[p, Length[p]] && ! MemberQ[p, d[p]]], {n, 0, z}]  (* A241380 *) Table[Count[f[n], p_ /; MemberQ[p, Length[p]] || MemberQ[p, d[p]]], {n, 0, z}] (* A241381 *) CROSSREFS Cf. A241378, A241379, A241380, A241381. Sequence in context: A063595 A316080 A130082 * A266750 A143065 A192660 Adjacent sequences:  A241374 A241375 A241376 * A241378 A241379 A241380 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 21 2014 STATUS approved

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Last modified May 31 12:48 EDT 2020. Contains 334748 sequences. (Running on oeis4.)