A240540 Number of partitions n such that the multiplicity of the number of even parts is a part.

0, 0, 0, 1, 2, 2, 2, 5, 7, 8, 13, 17, 26, 31, 43, 55, 76, 98, 125, 161, 206, 261, 331, 417, 518, 648, 805, 995, 1229, 1508, 1848, 2255, 2751, 3335, 4044, 4884, 5892, 7084, 8510, 10183, 12179, 14524, 17299, 20555, 24398, 28885, 34169, 40337, 47551, 55961

Offset

0,5

Links

Table of n, a(n) for n=0..49.

Example

a(7) counts these 5 partitions:  61, 421, 322, 3211, 22111; e.g., 421 has 2 even parts, and the multiplicity of 2 is 1, which is a part of 421.

Mathematica

z = 60; f[n_] := f[n] = IntegerPartitions[n];
Table[Count[f[n], p_ /; MemberQ[p, Count[p, Count[Mod[p, 2], 0]]]], {n, 0, z}]  (* A240540 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, Count[Mod[p, 2], 1]]]], {n, 0, z}]  (* A240541 *)

Crossrefs

Cf. A240541.

Sequence in context: A023569 A263373 A145876 * A039878 A365616 A162145

Adjacent sequences: A240537 A240538 A240539 * A240541 A240542 A240543

Keyword

nonn,easy

Author

Clark Kimberling, Apr 07 2014

Status

approved