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A240221
Number of partitions p of n such that median(p) >= mean(p).
6
1, 2, 3, 4, 5, 8, 7, 12, 14, 18, 18, 31, 27, 45, 53, 56, 63, 105, 99, 157, 160, 171, 216, 332, 319, 407, 533, 606, 610, 900, 832, 1213, 1434, 1649, 2172, 2399, 2042, 2901, 3849, 4533, 4623, 6340, 6430, 8724, 9450, 8745, 11511, 15449, 15485, 18695, 21716
OFFSET
1,2
FORMULA
a(n) = A240219(n) + A240220(n) for n >= 1.
a(n) + A240221(n) = A000041(n) for n >= 1.
EXAMPLE
a(8) counts these 3 partitions: 431, 332, 22211.
MATHEMATICA
z = 60; f[n_] := f[n] = IntegerPartitions[n];
Table[Count[f[n], p_ /; Median[p] < Mean[p]], {n, 1, z}] (* A240217 *)
Table[Count[f[n], p_ /; Median[p] <= Mean[p]], {n, 1, z}] (* A240218 *)
Table[Count[f[n], p_ /; Median[p] == Mean[p]], {n, 1, z}] (* A240219 *)
Table[Count[f[n], p_ /; Median[p] > Mean[p]], {n, 1, z}] (* A240220 *)
Table[Count[f[n], p_ /; Median[p] >= Mean[p]], {n, 1, z}] (* A240221 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 04 2014
STATUS
approved