A240867 Number of partitions of n into distinct parts of which the number of odd parts is a part and the number of even parts is not a part.

0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 3, 2, 5, 2, 7, 4, 12, 5, 16, 8, 23, 11, 32, 17, 43, 25, 56, 36, 73, 51, 93, 74, 118, 102, 150, 140, 188, 191, 236, 255, 294, 337, 369, 442, 458, 570, 574, 732, 716, 930, 894, 1174, 1113, 1467, 1389, 1830, 1727, 2259

Offset

0,12

Links

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

Example

a(13) counts these 3 partitions:  931, 841, 6421.

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, A240866, A240868; for analogous sequences for unrestricted partitions, see A240573-A240579.

Sequence in context: A111079 A165006 A134735 * A242363 A050360 A175003

Adjacent sequences: A240864 A240865 A240866 * A240868 A240869 A240870

Keyword

nonn,easy

Author

Clark Kimberling, Apr 14 2014

Status

approved