A240175 - OEIS

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

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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 *)