A240870 Number of partitions of n into distinct parts of which the number of odd parts is not a part.

0, 0, 1, 1, 2, 2, 3, 3, 5, 5, 7, 7, 11, 11, 15, 16, 22, 23, 31, 32, 42, 45, 58, 62, 79, 84, 106, 114, 140, 151, 187, 201, 244, 265, 319, 346, 413, 449, 533, 580, 683, 744, 873, 951, 1106, 1209, 1400, 1529, 1764, 1927, 2212, 2418, 2763, 3021, 3442, 3763, 4270

Offset

0,5

Links

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

Formula

a(n) + A240574(n) = A000009(n) for n >= 1.

Example

a(9) counts these 5 partitions:  9, 72, 63, 54, 432.

Mathematica

z = 40; 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}] (* A240869 *)
    t2 = Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240870 *)

Crossrefs

Cf. A240869, A240573, A000009.

Sequence in context: A321523 A226748 A119620 * A265771 A239513 A029018

Adjacent sequences: A240867 A240868 A240869 * A240871 A240872 A240873

Keyword

nonn,easy

Author

Clark Kimberling, Apr 14 2014

Status

approved