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A240875 Number of partitions p of n into distinct parts such that median(p) < mean(p). 0
0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 3, 4, 4, 8, 8, 11, 16, 20, 20, 32, 32, 44, 53, 66, 68, 89, 105, 127, 146, 172, 179, 253, 269, 306, 352, 403, 481, 577, 616, 694, 793, 965, 1028, 1243, 1334, 1482, 1811, 2008, 2143, 2468, 2765, 3208, 3629, 4021, 4311, 4905, 5493 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,11
LINKS
EXAMPLE
a(11) counts these 4 partitions: 821, 731, 632, 3321; e.g., median(p) = 3 < 11/3 = mean(p) for p = {6,3,2}.
MATHEMATICA
z = 70; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &]; Table[Count[f[n], p_ /; Median[p] < Mean[p]], {n, 0, z}]
CROSSREFS
Cf. A240217.
Sequence in context: A146944 A294113 A339827 * A127735 A330249 A075550
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 14 2014
STATUS
approved

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Last modified July 23 11:07 EDT 2024. Contains 374549 sequences. (Running on oeis4.)