A240574 Number of partitions of n such that the number of odd parts is a part.

0, 1, 0, 1, 1, 3, 2, 5, 6, 11, 11, 18, 23, 34, 40, 55, 73, 95, 120, 150, 202, 244, 320, 376, 511, 588, 784, 885, 1205, 1340, 1802, 1978, 2691, 2922, 3938, 4235, 5745, 6130, 8255, 8745, 11815, 12442, 16709, 17501, 23531, 24533, 32820, 34075, 45581, 47156

Offset

0,6

Links

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

Example

a(8) counts these 6 partitions:  521, 4211, 41111, 332, 3221, 22211.

Mathematica

z = 62; f[n_] := f[n] = IntegerPartitions[n];
Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]]], {n, 0, z}]  (* A240573 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}]  (* A240574 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] && MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}]  (* A240575 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] || MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240576 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] && ! MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}]  (* A240577 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 0]] && MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}]  (* A240578 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 0]] && ! MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}]  (* A240579 *)

Crossrefs

Cf. A240573, A240575, A240576, A240577, A240578, A240579.

Sequence in context: A308410 A286111 A338209 * A050061 A058638 A201218

Adjacent sequences: A240571 A240572 A240573 * A240575 A240576 A240577

Keyword

nonn,easy

Author

Clark Kimberling, Apr 10 2014

Status

approved