A240575 Number of partitions of n such that the number of even parts is a part and the number of odd parts is a part.

0, 0, 0, 1, 1, 2, 2, 3, 4, 5, 8, 10, 14, 16, 25, 28, 40, 47, 65, 77, 101, 122, 158, 193, 239, 295, 363, 449, 539, 670, 800, 989, 1169, 1439, 1701, 2083, 2442, 2975, 3493, 4224, 4941, 5944, 6955, 8313, 9706, 11538, 13475, 15936, 18568, 21859, 25466, 29847

Offset

0,6

Links

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

Example

a(10) counts these 8 partitions:  721, 6211, 5221, 4321, 43111, 421111, 3322, 32221.

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, A240576, A240577, A240578, A240579.

Sequence in context: A186505 A228693 A116676 * A176538 A285261 A100483

Adjacent sequences: A240572 A240573 A240574 * A240576 A240577 A240578

Keyword

nonn,easy

Author

Clark Kimberling, Apr 10 2014

Status

approved