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

1, 2, 3, 4, 5, 8, 7, 12, 14, 18, 18, 31, 27, 45, 53, 56, 63, 105, 99, 157, 160, 171, 216, 332, 319, 407, 533, 606, 610, 900, 832, 1213, 1434, 1649, 2172, 2399, 2042, 2901, 3849, 4533, 4623, 6340, 6430, 8724, 9450, 8745, 11511, 15449, 15485, 18695, 21716

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, A240220, 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) + A240220(n) for n >= 1.

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