A240218 - OEIS

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A240218

Number of partitions p of n such that median(p) <= mean(p).

1, 2, 3, 5, 6, 11, 13, 19, 26, 38, 45, 70, 82, 112, 154, 203, 244, 336, 402, 541, 700, 878, 1052, 1386, 1708, 2095, 2624, 3328, 3971, 5071, 6027, 7377, 9013, 10783, 13220, 16597, 19615, 23277, 27939, 34043, 39982, 48546, 56854, 68240, 82828, 97099, 113268

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..47.

FORMULA

a(n) + A240220(n) = A000041(n) for n >= 1.

a(n) = A240217(n) + A240219(n) for n >= 1.

EXAMPLE

a(6) counts these 11 partitions: 6, 51, 42, 411, 33, 321, 3111, 222, 2211, 21111, 111111.

MATHEMATICA

z = 60; f[n_] := f[n] = IntegerPartitions[n];