A240176 Number of partitions of n such that (least part) > (multiplicity of least part).

1, 0, 1, 1, 1, 2, 3, 3, 5, 5, 8, 10, 13, 15, 21, 25, 31, 39, 50, 59, 75, 89, 111, 134, 164, 194, 240, 285, 344, 410, 493, 582, 699, 824, 981, 1157, 1369, 1606, 1901, 2223, 2613, 3054, 3579, 4166, 4871, 5658, 6590, 7645, 8877, 10264, 11900, 13733, 15868

Offset

0,6

Links

Table of n, a(n) for n=0..52.

Formula

a(n) + A240175(n) + A096403(n) = A000041(n), for n >= 0.

Example

a(8) counts these 5 partitions:  8, 61, 53, 44, 332.

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 *)

Crossrefs

Cf. A188216, A096403, A240175, A240177.

Sequence in context: A058690 A290369 A087153 * A134408 A051032 A106530

Adjacent sequences: A240173 A240174 A240175 * A240177 A240178 A240179

Keyword

nonn,easy

Author

Clark Kimberling, Apr 02 2014

Status

approved