A240217 - OEIS

%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