A240215 Number of partitions p of n such that median(p) > multiplicity(min(p)).

0, 0, 1, 2, 2, 4, 5, 7, 9, 12, 18, 25, 32, 44, 57, 74, 95, 123, 155, 199, 248, 314, 394, 494, 610, 762, 939, 1158, 1419, 1743, 2117, 2584, 3127, 3793, 4573, 5513, 6615, 7950, 9503, 11360, 13532, 16123, 19133, 22709, 26863, 31769, 37477, 44176, 51939, 61048

Offset

0,4

Links

Table of n, a(n) for n=0..49.

Formula

a(n) = A240216(n) - A240214(n) for n >= 0.

a(n) + A240212(n) + A240214(n) = A000041(n) for n >= 0.

Example

a(6) counts these 9 partitions:  8, 71, 62, 53, 521, 44, 431, 332, 321.

Mathematica

z = 40; f[n_] := f[n] = IntegerPartitions[n]; t1 = Table[Count[f[n], p_ /; Median[p] < Count[p, Min[p]]], {n, 0, z}]  (* A240212 *)
t2 = Table[Count[f[n], p_ /; Median[p] <= Count[p, Min[p]]], {n, 0, z}] (* A240213 *)
t3 = Table[Count[f[n], p_ /; Median[p] == Count[p, Min[p]]], {n, 0, z}] (* A240214 *)
t4 = Table[Count[f[n], p_ /; Median[p] > Count[p, Min[p]]], {n, 0, z}] (* A240215 *)
t5 = Table[Count[f[n], p_ /; Median[p] >= Count[p, Min[p]]], {n, 0, z}] (* A240216 *)

Crossrefs

Cf. A240212, A240213, A240214, A240216, A000041.

Sequence in context: A258318 A027592 A007209 * A166239 A058661 A094362

Adjacent sequences: A240212 A240213 A240214 * A240216 A240217 A240218

Keyword

nonn,easy

Author

Clark Kimberling, Apr 04 2014

Status

approved