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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
OFFSET
1,5
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 04 2014
STATUS
approved