A240201 Number of partitions p of n such that mean(p) <= multiplicity(max(p)).

0, 1, 1, 1, 2, 2, 3, 3, 5, 6, 8, 9, 13, 14, 19, 22, 29, 33, 44, 47, 63, 71, 87, 100, 130, 138, 175, 202, 242, 272, 340, 365, 460, 516, 601, 687, 847, 891, 1095, 1249, 1440, 1600, 1943, 2085, 2529, 2816, 3185, 3621, 4356, 4555, 5456, 6166, 6952, 7691, 9156

Offset

0,5

Links

Table of n, a(n) for n=0..54.

Formula

a(n) = A240201(n) + A116900(n) for n >= 1.

a(n) + A240202(n) = A000041(n) for n >= 0.

Example

a(6) counts these 3 partitions:  222, 2211, 111111.

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, A240202, A116900, A116901, A000041.

Sequence in context: A035577 A002723 A035937 * A274158 A020999 A309712

Adjacent sequences: A240198 A240199 A240200 * A240202 A240203 A240204

Keyword

nonn,easy

Author

Clark Kimberling, Apr 03 2014

Status

approved