A240866 Number of partitions of n into distinct parts of which the number of even parts is a part and the number of odd parts is not a part.

0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 3, 2, 4, 3, 5, 6, 6, 8, 8, 13, 10, 18, 14, 26, 19, 34, 26, 47, 37, 59, 50, 77, 70, 98, 95, 125, 129, 157, 171, 198, 230, 247, 299, 310, 391, 388, 503, 483, 647, 604, 816, 754, 1034, 939, 1291, 1172, 1610, 1458, 1989, 1813, 2454

Offset

0,9

Links

Table of n, a(n) for n=0..60.

Example

a(10) counts these 3 partitions:  82, 631, 541.

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, A240865, A240867, A204868; for analogous sequences for unrestricted partitions, see A240573-A240579.

Sequence in context: A143619 A029141 A257880 * A230560 A265253 A161227

Adjacent sequences: A240863 A240864 A240865 * A240867 A240868 A240869

Keyword

nonn,easy

Author

Clark Kimberling, Apr 14 2014

Status

approved