A240577 Number of partitions of n such that the number of even parts is a part and the number of odd parts is not a part.

0, 0, 0, 0, 1, 1, 3, 4, 6, 10, 13, 18, 24, 35, 42, 61, 76, 102, 127, 168, 209, 271, 336, 424, 531, 661, 818, 1008, 1251, 1520, 1875, 2268, 2783, 3349, 4083, 4885, 5938, 7078, 8539, 10154, 12203, 14456, 17281, 20427, 24312, 28670, 33968, 39951, 47176, 55363

Offset

0,7

Links

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

Example

a(7) counts these 4 partitions:  4111, 322, 22111, 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, A240576, A240578, A240579.

Sequence in context: A344516 A310001 A310002 * A365614 A074321 A253049

Adjacent sequences: A240574 A240575 A240576 * A240578 A240579 A240580

Keyword

nonn,easy

Author

Clark Kimberling, Apr 10 2014

Status

approved