A240578 Number of partitions of n such that the number of odd parts is a part and the number of even parts is not a part.

0, 1, 0, 0, 0, 1, 0, 2, 2, 6, 3, 8, 9, 18, 15, 27, 33, 48, 55, 73, 101, 122, 162, 183, 272, 293, 421, 436, 666, 670, 1002, 989, 1522, 1483, 2237, 2152, 3303, 3155, 4762, 4521, 6874, 6498, 9754, 9188, 13825, 12995, 19345, 18139, 27013, 25297, 37332, 34909

Offset

0,8

Links

Table of n, a(n) for n=0..51.

Example

a(9) counts these 6 partitions:  531, 51111, 441, 4221, 333, 22221.

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, A240574, A240575, A240576, A240577, A240579.

Sequence in context: A344469 A308159 A081745 * A273105 A370370 A307966

Adjacent sequences: A240575 A240576 A240577 * A240579 A240580 A240581

Keyword

nonn,easy

Author

Clark Kimberling, Apr 10 2014

Status

approved