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A240175 Number of partitions of n such that the least part is less than its multiplicity. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A030013 A130404 A064689 * A238590 A144120 A073712

Adjacent sequences:  A240172 A240173 A240174 * A240176 A240177 A240178

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 02 2014

STATUS

approved

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Last modified July 10 11:42 EDT 2020. Contains 335576 sequences. (Running on oeis4.)