A240219 - OEIS

A240219

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

1, 2, 3, 4, 4, 8, 5, 9, 10, 14, 7, 24, 8, 22, 31, 28, 10, 56, 11, 71, 68, 47, 13, 143, 69, 66, 147, 216, 16, 367, 17, 241, 304, 122, 509, 1019, 20, 163, 603, 1238, 22, 1712, 23, 1789, 3144, 286, 25, 3956, 1581, 2481, 2101, 4638, 28, 7739, 7357, 9209, 3737

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..57.

FORMULA

a(n) = A240218(n) - A240217(n) for n >= 1.

a(n) + A240217(n) + A240220 = A000041(n) for n >= 1.

EXAMPLE

a(6) counts these 8 partitions: 6, 51, 42, 33, 331, 222, 2211, 111111.

MATHEMATICA

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