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A240304 Number of partitions of n such that (maximal multiplicity of parts) > (multiplicity of the least part). 2
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 (list; graph; refs; listen; history; text; internal format)
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 A281597 A039007

Adjacent sequences:  A240301 A240302 A240303 * A240305 A240306 A240307

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 04 2014

STATUS

approved

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Last modified September 17 10:37 EDT 2019. Contains 327129 sequences. (Running on oeis4.)