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

0,5

Links

Table of n, a(n) for n=0..47.

Formula

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

Example

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

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 *)

Crossrefs

Cf. A188216, A096403, A240176, A240177.

Sequence in context: A362009 A365411 A064689 * A238590 A144120 A073712

Adjacent sequences: A240172 A240173 A240174 * A240176 A240177 A240178

Keyword

nonn,easy

Author

Clark Kimberling, Apr 02 2014

Status

approved