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%I #7 Apr 15 2014 14:38:56
%S 0,0,0,1,2,3,8,10,16,24,38,46,74,90,123,175,234,280,391,470,632,831,
%T 1039,1243,1639,2029,2477,3112,3955,4704,6010,7136,8709,10661,12711,
%U 15578,19595,23114,27336,32805,39960,46834,56831,66451,79684,96813,113243
%N Number of partitions p of n such that median(p) < mean(p).
%F a(n) = A240219(n) - A240218(n) for n >= 1.
%F a(n) + A240221(n) = A000041(n) for n >= 1.
%e a(6) counts these 3 partitions: 411, 3111, 21111.
%t z = 60; f[n_] := f[n] = IntegerPartitions[n];
%t Table[Count[f[n], p_ /; Median[p] < Mean[p]], {n, 1, z}] (* A240217 *)
%t Table[Count[f[n], p_ /; Median[p] <= Mean[p]], {n, 1, z}] (* A240218 *)
%t Table[Count[f[n], p_ /; Median[p] == Mean[p]], {n, 1, z}] (* A240219 *)
%t Table[Count[f[n], p_ /; Median[p] > Mean[p]], {n, 1, z}] (* A240220 *)
%t Table[Count[f[n], p_ /; Median[p] >= Mean[p]], {n, 1, z}] (* A240221 *)
%Y Cf. A240218, A240219, A240220, A240221, A000041.
%K nonn,easy
%O 1,5
%A _Clark Kimberling_, Apr 04 2014
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