A240206 Number of partitions p of n such that mean(p) > multiplicity(min(p)).

0, 0, 1, 2, 2, 4, 5, 9, 11, 16, 22, 31, 39, 56, 71, 91, 123, 157, 195, 263, 324, 405, 529, 649, 790, 1032, 1253, 1514, 1902, 2357, 2826, 3497, 4179, 5153, 6279, 7459, 8880, 11079, 13089, 15435, 18438, 22596, 26514, 31423, 36783, 44336, 52827, 61570, 71653

Offset: 0

Author

Clark Kimberling, Apr 03 2014

Keywords

• nonn
• easy

Examples

			a(6) counts these 5 partitions:  6, 51, 42, 33, 321.
		

Crossrefs

Cf. A240203, A240204, A240205, A240079, A000041.

Programs

Mathematica

z = 60; f[n_] := f[n] = IntegerPartitions[n];
t1 = Table[Count[f[n], p_ /; Mean[p] < Count[p, Min[p]]], {n, 0, z}]  (* A240203 *)
t2 = Table[Count[f[n], p_ /; Mean[p] <= Count[p, Min[p]]], {n, 0, z}] (* A240204 *)
t3 = Table[Count[f[n], p_ /; Mean[p] == Count[p, Min[p]]], {n, 0, z}] (* A240205 *)
t4 = Table[Count[f[n], p_ /; Mean[p] > Count[p, Min[p]]], {n, 0, z}] (* A240206 *)
t5 = Table[Count[f[n], p_ /; Mean[p] >= Count[p, Min[p]]], {n, 0, z}] (* A240079 *)

Formula

a(n) = A240079(n) - A240205(n) for n >= 0.

a(n) + A240203(n) + A240205(n) = A000041(n) for n >= 0.