A240303 Number of partitions of n such that (maximal multiplicity of parts) = (multiplicity of the least part).

0, 1, 2, 3, 5, 6, 11, 13, 19, 26, 37, 44, 66, 80, 108, 139, 182, 226, 298, 366, 474, 588, 742, 911, 1154, 1408, 1751, 2143, 2642, 3205, 3944, 4761, 5805, 6998, 8479, 10177, 12285, 14679, 17620, 21014, 25114, 29822, 35529, 42057, 49894, 58927, 69644, 81994

Offset

0,3

Links

Table of n, a(n) for n=0..47.

Formula

a(n) + A240304(n) = A000041(n) for n >= 1.

Example

a(7) counts all the 15 partitions of 7 except 331 and 2221, so that a(7) = 13.

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. A240304, A000041, A171979.

Sequence in context: A171040 A317256 A100883 * A240218 A347414 A317707

Adjacent sequences: A240300 A240301 A240302 * A240304 A240305 A240306

Keyword

nonn,easy

Author

Clark Kimberling, Apr 04 2014

Status

approved