A240864 Number of partitions of n into distinct parts of which the number of even parts and the number of odd parts are parts.

0, 0, 0, 1, 0, 1, 1, 2, 1, 2, 2, 3, 3, 4, 5, 6, 8, 8, 11, 10, 17, 15, 23, 19, 32, 26, 42, 35, 57, 49, 73, 66, 95, 90, 119, 121, 153, 161, 191, 214, 239, 280, 298, 365, 373, 470, 462, 603, 576, 763, 714, 963, 889, 1205, 1102, 1502, 1371, 1857, 1696, 2289

Offset

0,8

Links

Table of n, a(n) for n=0..59.

Example

a(15) counts these 6 partitions:  {14,1}, {12,2,1}, {9,3,2,1}, {7,4,3,1}, {6,5,3,1}, {5,4,3,2,1}.

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, A240865, A240866, A240867, A204868; for analogous sequences for unrestricted partitions, see A240573-A240579.

Sequence in context: A161228 A214130 A029172 * A241322 A275380 A161052

Adjacent sequences: A240861 A240862 A240863 * A240865 A240866 A240867

Keyword

nonn,easy

Author

Clark Kimberling, Apr 14 2014

Status

approved