A240183 Number of partitions of n such that (greatest part) = (multiplicity of least part).

0, 1, 0, 0, 2, 0, 2, 0, 3, 3, 4, 2, 9, 3, 10, 10, 17, 11, 26, 19, 36, 33, 48, 47, 79, 71, 101, 109, 149, 151, 215, 216, 293, 318, 404, 443, 575, 611, 773, 864, 1068, 1175, 1458, 1609, 1964, 2210, 2642, 2970, 3577, 3995, 4753, 5369, 6332, 7138, 8414, 9476

Offset

0,5

Links

Table of n, a(n) for n=0..55.

Formula

A240178(n) + a(n) + A240184(n) = A000041(n) for n >= 0.

Example

a(8) counts these 3 partitions:  41111, 32111, 22211.

Mathematica

z = 60; f[n_] := f[n] = IntegerPartitions[n];
t1 = Table[Count[f[n], p_ /; Max[p] < Count[p, Min[p]]], {n, 0, z}]  (* A240178 except for n=0 *)
t2 = Table[Count[f[n], p_ /; Max[p] <= Count[p, Min[p]]], {n, 0, z}] (* A240182 *)
t3 = Table[Count[f[n], p_ /; Max[p] == Count[p, Min[p]]], {n, 0, z}] (* A240183 *)
t4 = Table[Count[f[n], p_ /; Max[p] > Count[p, Min[p]]], {n, 0, z}] (* A240184 *)
t5 = Table[Count[f[n], p_ /; Max[p] >= Count[p, Min[p]]], {n, 0, z}] (* A240179 *)

Crossrefs

Cf. A240178, A240182, A240184, A240179, A000041.

Sequence in context: A316432 A046522 A242896 * A112631 A158706 A096500

Adjacent sequences: A240180 A240181 A240182 * A240184 A240185 A240186

Keyword

nonn,easy

Author

Clark Kimberling, Apr 02 2014

Status

approved