A240576 Number of partitions of n such that the number of even parts is a part or the number of odd parts is a part.

0, 1, 0, 1, 2, 4, 5, 9, 12, 21, 24, 36, 47, 69, 82, 116, 149, 197, 247, 318, 411, 515, 656, 800, 1042, 1249, 1602, 1893, 2456, 2860, 3677, 4246, 5474, 6271, 8021, 9120, 11683, 13208, 16794, 18899, 24018, 26898, 33990, 37928, 47843, 53203, 66788, 74026, 92757

Offset

0,5

Links

Table of n, a(n) for n=0..48.

Example

a(6) counts these 5 partitions:  42, 411, 321, 2211, 21111.

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, A240577, A240578, A240579.

Sequence in context: A083690 A241824 A144121 * A060312 A218934 A348176

Adjacent sequences: A240573 A240574 A240575 * A240577 A240578 A240579

Keyword

nonn,easy

Author

Clark Kimberling, Apr 10 2014

Status

approved