A240175 Number of partitions of n such that the least part is less than its multiplicity.

0, 0, 1, 1, 2, 3, 6, 7, 12, 16, 24, 32, 47, 60, 84, 110, 148, 191, 254, 323, 423, 535, 687, 864, 1100, 1371, 1726, 2141, 2669, 3290, 4075, 4990, 6136, 7481, 9137, 11087, 13471, 16264, 19659, 23641, 28438, 34060, 40801, 48676, 58074, 69049, 82064, 97246

Offset: 0

Author

Clark Kimberling, Apr 02 2014

Keywords

• nonn
• easy

Examples

			a(8) counts these 12 partitions:  611, 5111, 4211, 41111, 3311, 32111, 311111, 2222, 22211, 221111, 2111111, 11111111.
		

Crossrefs

Cf. A188216, A096403, A240176, A240177.

Programs

Mathematica

z = 60; f[n_] := f[n] = IntegerPartitions[n];
Table[Count[f[n], p_ /; Min[p] < Count[p, Min[p]]], {n, 0, z}](* A240175 *)
Table[Count[f[n], p_ /; Min[p] <= Count[p, Min[p]]], {n, 0, z}](* A188216 *)
Table[Count[f[n], p_ /; Min[p] == Count[p, Min[p]]], {n, 0, z}](* A096403 *)
Table[Count[f[n], p_ /; Min[p] > Count[p, Min[p]]], {n, 0, z}] (* A240176 *)
Table[Count[f[n], p_ /; Min[p] >= Count[p, Min[p]]], {n, 0, z}] (* A240177 *)

Formula

a(n) = A188216(n) - A096403(n), for n >= 0.