A240304 Number of partitions of n such that (maximal multiplicity of parts) > (multiplicity of the least part).

0, 0, 0, 0, 0, 1, 0, 2, 3, 4, 5, 12, 11, 21, 27, 37, 49, 71, 87, 124, 153, 204, 260, 344, 421, 550, 685, 867, 1076, 1360, 1660, 2081, 2544, 3145, 3831, 4706, 5692, 6958, 8395, 10171, 12224, 14761, 17645, 21204, 25281, 30207, 35914, 42760, 50618, 60057, 70914

Offset

0,8

Links

Table of n, a(n) for n=0..50.

Formula

a(n) + A240303(n) = A000041(n) for n >= 1.

Example

a(7) counts these 2 partitions of 7: 331, 2221.

Mathematica

z = 60; f[n_] := f[n] = IntegerPartitions[n]; m[p_] := Max[Map[Length, Split[p]]] (* maximal multiplicity *)
Table[Count[f[n], p_ /; m[p] == Count[p, Min[p]]], {n, 0, z}] (* A240303 *)
Table[Count[f[n], p_ /; m[p] > Count[p, Min[p]]], {n, 0, z}] (* A240304 *)

Crossrefs

Cf. A240303, A000041, A171979.

Sequence in context: A143482 A193679 A066574 * A325684 A339453 A281597

Adjacent sequences: A240301 A240302 A240303 * A240305 A240306 A240307

Keyword

nonn,easy

Author

Clark Kimberling, Apr 04 2014

Status

approved