cp's OEIS Frontend

A240221 Number of partitions p of n such that median(p) >= mean(p).

%I A240221 #7 Apr 15 2014 14:38:05
%S A240221 1,2,3,4,5,8,7,12,14,18,18,31,27,45,53,56,63,105,99,157,160,171,216,
%T A240221 332,319,407,533,606,610,900,832,1213,1434,1649,2172,2399,2042,2901,
%U A240221 3849,4533,4623,6340,6430,8724,9450,8745,11511,15449,15485,18695,21716
%N A240221 Number of partitions p of n such that median(p) >= mean(p).
%F A240221 a(n) = A240219(n) + A240220(n) for n >= 1.
%F A240221 a(n) + A240221(n) = A000041(n) for n >= 1.
%e A240221 a(8) counts these 3 partitions:  431, 332, 22211.
%t A240221 z = 60; f[n_] := f[n] = IntegerPartitions[n];
%t A240221 Table[Count[f[n], p_ /; Median[p] < Mean[p]], {n, 1, z}]  (* A240217 *)
%t A240221 Table[Count[f[n], p_ /; Median[p] <= Mean[p]], {n, 1, z}] (* A240218 *)
%t A240221 Table[Count[f[n], p_ /; Median[p] == Mean[p]], {n, 1, z}] (* A240219 *)
%t A240221 Table[Count[f[n], p_ /; Median[p] > Mean[p]], {n, 1, z}]  (* A240220 *)
%t A240221 Table[Count[f[n], p_ /; Median[p] >= Mean[p]], {n, 1, z}] (* A240221 *)
%Y A240221 Cf. A240217, A240218, A240219, A240220, A000041.
%K A240221 nonn,easy
%O A240221 1,2
%A A240221 _Clark Kimberling_, Apr 04 2014