A240202 Number of partitions p of n such that mean(p) > multiplicity(max(p)).

0, 0, 1, 2, 3, 5, 8, 12, 17, 24, 34, 47, 64, 87, 116, 154, 202, 264, 341, 443, 564, 721, 915, 1155, 1445, 1820, 2261, 2808, 3476, 4293, 5264, 6477, 7889, 9627, 11709, 14196, 17130, 20746, 24920, 29936, 35898, 42983, 51231, 61176, 72646, 86318, 102373, 121133

Offset

0,4

Links

Table of n, a(n) for n=0..47.

Formula

A240200(n) + A116900(n) + a(n) = A000041(n) for n >= 1.

Example

a(6) counts these 8 partitions:  6, 51, 42, 411, 33, 321, 3111, 21111.

Mathematica

z = 60; f[n_] := f[n] = IntegerPartitions[n];
t1 = Table[Count[f[n], p_ /; Mean[p] < Count[p, Max[p]]], {n, 0, z}]  (* A240200 *)
t2 = Table[Count[f[n], p_ /; Mean[p] <= Count[p, Max[p]]], {n, 0, z}] (* A240201 *)
t3 = Table[Count[f[n], p_ /; Mean[p] == Count[p, Max[p]]], {n, 0, z}] (* A116900 *)
t4 = Table[Count[f[n], p_ /; Mean[p] > Count[p, Max[p]]], {n, 0, z}] (* A240202 *)
t5 = Table[Count[f[n], p_ /; Mean[p] >= Count[p, Max[p]]], {n, 0, z}] (* A116901 *)

Crossrefs

Cf. A240200, A240201, A116900, A116901, A000041.

Sequence in context: A061535 A280276 A233969 * A235945 A129504 A241553

Adjacent sequences: A240199 A240200 A240201 * A240203 A240204 A240205

Keyword

nonn,easy

Author

Clark Kimberling, Apr 03 2014

Status

approved