A240875 Number of partitions p of n into distinct parts such that median(p) < mean(p).

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

Offset

0,11

Links

Table of n, a(n) for n=0..56.

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

Adjacent sequences: A240872 A240873 A240874 * A240876 A240877 A240878

Keyword

nonn,easy

Author

Clark Kimberling, Apr 14 2014

Status

approved