A239947 Number of partitions of n containing 2*h as a part, where h is the number of distinct parts.

0, 0, 1, 0, 1, 1, 3, 2, 3, 4, 9, 9, 12, 16, 23, 24, 37, 48, 62, 78, 100, 114, 157, 195, 241, 302, 375, 451, 584, 695, 844, 1040, 1265, 1519, 1865, 2236, 2728, 3264, 3903, 4660, 5613, 6667, 7935, 9462, 11246, 13209, 15731, 18564, 21885, 25787, 30295, 35535

Offset

0,7

Links

Table of n, a(n) for n=0..51.

Example

a(11) counts these 9 partitions:  74, 641, 632, 6311, 6221, 62111, 443, 44111, 41111111.

Mathematica

z = 60; d[p_] := d[p] = Length[DeleteDuplicates[p]];  Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, 2*d[p]]], {n, 0, z}]

Crossrefs

Cf. A239945.

Sequence in context: A201907 A003559 A200599 * A173093 A236361 A227634

Adjacent sequences: A239944 A239945 A239946 * A239948 A239949 A239950

Keyword

nonn,easy

Author

Clark Kimberling, Mar 30 2014

Status

approved