A240865 Number of partitions of n into distinct parts of which the number of even parts or the number of odd parts is a part.

0, 1, 0, 1, 0, 1, 2, 2, 3, 4, 6, 7, 8, 10, 12, 17, 16, 23, 23, 35, 32, 49, 45, 68, 62, 92, 85, 125, 119, 164, 159, 216, 216, 281, 288, 364, 384, 468, 502, 600, 660, 763, 852, 969, 1101, 1227, 1407, 1544, 1793, 1941, 2262, 2433, 2853, 3038, 3567, 3787, 4448

Offset

0,7

Links

Table of n, a(n) for n=0..56.

Example

a(9)counts these 4 partitions: 81, 621, 531, 432.

Mathematica

 z = 70; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
    t1 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]]], {n, 0, z}] (* A240862 *)
    t2 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240863, *)
    t3 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] && MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240864 *)
    t4 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] || MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240865 *)
    t5 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] && ! MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240866 *)
    t6 = Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 0]] && MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240867 *)
    t7 = Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 0]] && ! MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240868 *)

Crossrefs

Cf. A240862, A240863, A240864, A240866, A240867, A204868; for analogous sequences for unrestricted partitions, see A240573-A240579.

Sequence in context: A075465 A011868 A145813 * A039859 A130291 A067835

Adjacent sequences: A240862 A240863 A240864 * A240866 A240867 A240868

Keyword

nonn,easy

Author

Clark Kimberling, Apr 14 2014

Status

approved