A240303 - OEIS

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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

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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 *)