A240177 Number of partitions of n such that (least part) >= (multiplicity of least part).

1, 1, 1, 2, 3, 4, 5, 8, 10, 14, 18, 24, 30, 41, 51, 66, 83, 106, 131, 167, 204, 257, 315, 391, 475, 587, 710, 869, 1049, 1275, 1529, 1852, 2213, 2662, 3173, 3796, 4506, 5373, 6356, 7544, 8900, 10523, 12373, 14585, 17101, 20085, 23494, 27508, 32087, 37471

Offset: 0

Author

Clark Kimberling, Apr 02 2014

Keywords

• nonn
• easy

Examples

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

Crossrefs

Cf. A188216, A096403, A240175, A240176.

Programs

Mathematica

z = 60; f[n_] := f[n] = IntegerPartitions[n]; t1 = Table[Count[f[n], p_ /; Min[p] < Count[p, Min[p]]], {n, 0, z}]  (* A240175 *)
t2 = Table[Count[f[n], p_ /; Min[p] <= Count[p, Min[p]]], {n, 0, z}] (* A188216 *)
t3 = Table[Count[f[n], p_ /; Min[p] == Count[p, Min[p]]], {n, 0, z}] (* A096403 *)
t4 = Table[Count[f[n], p_ /; Min[p] > Count[p, Min[p]]], {n, 0, z}] (* A240176 *)
t5 = Table[Count[f[n], p_ /; Min[p] >= Count[p, Min[p]]], {n, 0, z}] (* A240177 *)

Formula

a(n) = A096403(n) + A240176(n), for n >= 0.