A240217 Number of partitions p of n such that median(p) < mean(p).

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

Author

Clark Kimberling, Apr 04 2014

Keywords

• nonn
• easy

Examples

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

Crossrefs

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

Programs

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 *)

Formula

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

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