A239966 Number of partitions of n such that (number of distinct parts) = minimal multiplicity of the parts.

0, 1, 1, 1, 1, 1, 2, 2, 4, 3, 6, 5, 8, 6, 13, 6, 15, 10, 19, 12, 24, 15, 33, 22, 38, 28, 52, 39, 61, 51, 78, 66, 94, 85, 118, 103, 140, 130, 168, 165, 194, 190, 244, 230, 274, 285, 328, 327, 394, 386, 449, 485, 522, 540, 646, 639, 712, 790, 846, 880, 1025

Offset

0,7

Links

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

Example

a(8) counts these 4 partitions :  8, 3311, 22211, 221111.

Mathematica

z = 61; d[p_] := d[p] = Length[DeleteDuplicates[p]]; m[p_] := Min[Map[Length, Split[p]]]; Table[Count[IntegerPartitions[n], p_ /; d[p] == m[p]], {n, 0, z}]

Crossrefs

Cf. A239964, A239948.

Sequence in context: A060367 A267451 A062968 * A341465 A304406 A053197

Adjacent sequences: A239963 A239964 A239965 * A239967 A239968 A239969

Keyword

nonn,easy

Author

Clark Kimberling, Mar 30 2014

Status

approved