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A240217 Number of partitions p of n such that median(p) < mean(p). 6
0, 0, 0, 1, 2, 3, 8, 10, 16, 24, 38, 46, 74, 90, 123, 175, 234, 280, 391, 470, 632, 831, 1039, 1243, 1639, 2029, 2477, 3112, 3955, 4704, 6010, 7136, 8709, 10661, 12711, 15578, 19595, 23114, 27336, 32805, 39960, 46834, 56831, 66451, 79684, 96813, 113243 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..47.

FORMULA

a(n) = A240219(n) - A240218(n) for n >= 1.

a(n) + A240221(n) = A000041(n) for n >= 1.

EXAMPLE

a(6) counts these 3 partitions:  411, 3111, 21111.

MATHEMATICA

z = 60; f[n_] := f[n] = IntegerPartitions[n];

Table[Count[f[n], p_ /; Median[p] < Mean[p]], {n, 1, z}]  (* A240217 *)

Table[Count[f[n], p_ /; Median[p] <= Mean[p]], {n, 1, z}] (* A240218 *)

Table[Count[f[n], p_ /; Median[p] == Mean[p]], {n, 1, z}] (* A240219 *)

Table[Count[f[n], p_ /; Median[p] > Mean[p]], {n, 1, z}]  (* A240220 *)

Table[Count[f[n], p_ /; Median[p] >= Mean[p]], {n, 1, z}] (* A240221 *)

CROSSREFS

Cf. A240218, A240219, A240220, A240221, A000041.

Sequence in context: A317655 A060697 A326714 * A265224 A093353 A083799

Adjacent sequences:  A240214 A240215 A240216 * A240218 A240219 A240220

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 04 2014

STATUS

approved

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Last modified September 21 04:58 EDT 2020. Contains 337267 sequences. (Running on oeis4.)