A240220 Number of partitions p of n such that median(p) > mean(p).

0, 0, 0, 0, 1, 0, 2, 3, 4, 4, 11, 7, 19, 23, 22, 28, 53, 49, 88, 86, 92, 124, 203, 189, 250, 341, 386, 390, 594, 533, 815, 972, 1130, 1527, 1663, 1380, 2022, 2738, 3246, 3295, 4601, 4628, 6407, 6935, 6306, 8459, 11486, 11493, 13904, 16214, 19615, 21423

Offset: 1

Author

Clark Kimberling, Apr 04 2014

Keywords

• nonn
• easy

Examples

			a(8) counts these 3 partitions:  431, 332, 22211.
		

Crossrefs

Cf. A240217, A240218, A240219, 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) = A240221(n) - A240219(n) for n >= 1.

a(n) + A240218(n) = A000041(n) for n >= 1.