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A240310 Number of partitions p of n such that (maximal multiplicity of the parts of p) < maximal part of p). 5
0, 0, 1, 2, 2, 4, 6, 10, 14, 19, 27, 37, 50, 69, 92, 123, 161, 213, 273, 355, 453, 580, 734, 931, 1168, 1468, 1830, 2279, 2821, 3490, 4292, 5275, 6450, 7878, 9584, 11645, 14091, 17039, 20529, 24703, 29640, 35520, 42447, 50669, 60329, 71743, 85131, 100892 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

FORMULA

a(n) = A240311(n) - A240312(n) for n >= 0.

a(n) + A240312(n) + A240314(n) = A000041(n) for n >= 0.

EXAMPLE

a(6) counts these 6 partitions:  6, 51, 42, 411, 33, 321.

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] < Max[p]], {n, 0, z}]  (* A240310 *)

Table[Count[f[n], p_ /; m[p] <= Max[p]], {n, 0, z}] (* A240311 *)

Table[Count[f[n], p_ /; m[p] == Max[p]], {n, 0, z}] (* A240312 *)

Table[Count[f[n], p_ /; m[p] >= Max[p]], {n, 0, z}] (* A240313 *)

Table[Count[f[n], p_ /; m[p] > Max[p]], {n, 0, z}]  (* A240314*)

CROSSREFS

Cf. A240311, A240312, A240313, A240314, A000041.

Sequence in context: A236634 A034406 A098330 * A083848 A330644 A278297

Adjacent sequences:  A240307 A240308 A240309 * A240311 A240312 A240313

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 05 2014

STATUS

approved

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Last modified October 29 04:54 EDT 2020. Contains 338066 sequences. (Running on oeis4.)