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A240303 Number of partitions of n such that (maximal multiplicity of parts) = (multiplicity of the least part). 2
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 (list; graph; refs; listen; history; text; internal format)
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 A317707 A104012

Adjacent sequences:  A240300 A240301 A240302 * A240304 A240305 A240306

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 04 2014

STATUS

approved

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Last modified September 17 06:00 EDT 2019. Contains 327119 sequences. (Running on oeis4.)