A241132 Number of partitions p of n such that (maximal multiplicity over the parts of p) = (number of numbers in p having multiplicity > 1).

0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 4, 2, 5, 6, 10, 16, 17, 23, 32, 42, 53, 79, 88, 117, 146, 189, 230, 298, 374, 452, 562, 688, 842, 1036, 1256, 1520, 1876, 2225, 2688, 3226, 3875, 4608, 5528, 6553, 7799, 9272, 10936, 12903, 15239, 17919, 21038, 24714, 28922, 33819

Offset

0,11

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Example

a(10) counts these 4 partitions:  4411, 42211, 3322, 33211.

Mathematica

z = 30; e[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] > 1 &]]];
m[p_] := Max[Map[Length, Split[p]]]; Table[Count[IntegerPartitions[n], p_ /; m[p] == e[p]], {n, 0, z}]

Crossrefs

Cf. A241090, A241131.

Sequence in context: A109174 A160211 A035584 * A173921 A003572 A260623

Adjacent sequences: A241129 A241130 A241131 * A241133 A241134 A241135

Keyword

nonn,easy

Author

Clark Kimberling, Apr 24 2014

Status

approved