A240541 Number of partitions n such that the multiplicity of the number of odd parts is a part.

0, 1, 0, 1, 1, 3, 2, 4, 4, 11, 9, 16, 15, 30, 29, 48, 49, 81, 82, 125, 136, 203, 220, 306, 344, 476, 537, 710, 822, 1068, 1240, 1565, 1851, 2305, 2733, 3323, 3989, 4796, 5775, 6826, 8287, 9694, 11787, 13611, 16659, 19070, 23363, 26463, 32554, 36616, 45080

Offset

0,6

Links

Table of n, a(n) for n=0..50.

Example

a(7) counts these 4 partitions:  61, 421, 3211, 2221; e.g., 3211 has 3 odd parts, and the multiplicity of 3 is 1, which is a part of 3211.

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. A240540.

Sequence in context: A326923 A365613 A338315 * A073369 A021759 A070221

Adjacent sequences: A240538 A240539 A240540 * A240542 A240543 A240544

Keyword

nonn,easy

Author

Clark Kimberling, Apr 07 2014

Status

approved