A240200 Number of partitions p of n such that mean(p) < multiplicity(max(p)).

0, 0, 1, 1, 1, 2, 3, 3, 4, 5, 7, 9, 11, 14, 17, 21, 24, 33, 37, 47, 56, 67, 79, 100, 109, 137, 161, 189, 217, 272, 297, 365, 416, 485, 560, 685, 726, 891, 1029, 1176, 1314, 1600, 1728, 2085, 2336, 2637, 3020, 3621, 3802, 4554, 5171, 5820, 6461, 7691, 8266

Offset

0,6

Links

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

Formula

a(n) = A240201(n) - A116900(n) for n >= 0.

a(n) + A116900(n) + A240202(n) = A000041(n) for n >= 1.

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. A240201, A240202, A116900, A116901, A000041.

Sequence in context: A305631 A036019 A018120 * A094979 A065565 A309795

Adjacent sequences: A240197 A240198 A240199 * A240201 A240202 A240203

Keyword

nonn,easy

Author

Clark Kimberling, Apr 03 2014

Status

approved