A240579 Number of partitions of n such that the number of odd parts is not a part and the number of even parts is not a part.

1, 0, 2, 2, 3, 3, 6, 6, 10, 9, 18, 20, 30, 32, 53, 60, 82, 100, 138, 172, 216, 277, 346, 455, 533, 709, 834, 1117, 1262, 1705, 1927, 2596, 2875, 3872, 4289, 5763, 6294, 8429, 9221, 12286, 13320, 17685, 19184, 25333, 27332, 35931, 38770, 50728, 54516, 710069

Offset

0,3

Links

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

Example

a(7) counts these 6 partitions:  7, 52, 511, 43, 31111, 1111111.

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, A240578.

Sequence in context: A101199 A032155 A116932 * A292225 A238786 A238547

Adjacent sequences: A240576 A240577 A240578 * A240580 A240581 A240582

Keyword

nonn,easy

Author

Clark Kimberling, Apr 10 2014

Status

approved