A241545 Number of partitions p of n such that (number of odd numbers in p) is a part of p.

0, 1, 1, 2, 2, 4, 5, 8, 10, 17, 22, 31, 42, 59, 79, 106, 138, 181, 241, 305, 397, 499, 647, 794, 1021, 1249, 1595, 1921, 2435, 2914, 3678, 4366, 5469, 6464, 8064, 9469, 11734, 13737, 16957, 19754, 24267, 28188, 34482, 39929, 48622, 56158, 68143, 78485, 94831

Offset

0,4

Comments

Each number in p is counted once, regardless of its multiplicity.

Links

Table of n, a(n) for n=0..48.

Example

a(6) counts these 5 partitions:  411, 321, 2211, 21111, 111111.

Mathematica

z = 30; f[n_] := f[n] = IntegerPartitions[n]; s0[p_] := Count[Mod[DeleteDuplicates[p], 2],  0]; s1[p_] :=
Count[Mod[DeleteDuplicates[p], 2], 1];
Table[Count[f[n], p_ /; MemberQ[p, s0[p]]], {n, 0, z}]   (* A241544 *)
Table[Count[f[n], p_ /; MemberQ[p, s1[p]]], {n, 0, z}]   (* A241545 *)

Crossrefs

Cf. A241544.

Sequence in context: A325831 A240451 A206138 * A157162 A109434 A371840

Adjacent sequences: A241542 A241543 A241544 * A241546 A241547 A241548

Keyword

nonn,easy

Author

Clark Kimberling, Apr 26 2014

Status

approved