A240203 Number of partitions p of n such that mean(p) < multiplicity(min(p)).

0, 0, 1, 1, 2, 3, 5, 6, 9, 13, 18, 25, 34, 45, 62, 78, 105, 140, 173, 227, 298, 361, 471, 606, 725, 925, 1181, 1435, 1757, 2208, 2687, 3345, 4021, 4871, 6029, 7390, 8617, 10558, 12924, 15535, 18112, 21987, 26372, 31838, 37245, 43875, 52729, 63184, 73092

Offset

0,5

Links

Table of n, a(n) for n=0..48.

Formula

a(n) + A240205(n) + A240079(n) = A000041(n) for n >= 0.

Example

a(6) counts these 5 partitions:  3111, 222, 2211, 21111, 111111.

Mathematica

z = 60; f[n_] := f[n] = IntegerPartitions[n];
t1 = Table[Count[f[n], p_ /; Mean[p] < Count[p, Min[p]]], {n, 0, z}]  (* A240203 *)
t2 = Table[Count[f[n], p_ /; Mean[p] <= Count[p, Min[p]]], {n, 0, z}] (* A240204 *)
t3 = Table[Count[f[n], p_ /; Mean[p] == Count[p, Min[p]]], {n, 0, z}] (* A240205 *)
t4 = Table[Count[f[n], p_ /; Mean[p] > Count[p, Min[p]]], {n, 0, z}] (* A240206 *)
t5 = Table[Count[f[n], p_ /; Mean[p] >= Count[p, Min[p]]], {n, 0, z}] (* A240079 *)

Crossrefs

Cf. A240204, A240205, A240206, A240079, A000041.

Sequence in context: A240306 A094873 A240726 * A018126 A087900 A101216

Adjacent sequences: A240200 A240201 A240202 * A240204 A240205 A240206

Keyword

nonn,easy

Author

Clark Kimberling, Apr 03 2014

Status

approved