A240210 Number of partitions p of n such that median(p) > multiplicity(max(p)).

0, 0, 1, 2, 2, 3, 5, 8, 11, 16, 23, 30, 42, 57, 76, 102, 134, 177, 227, 298, 380, 488, 619, 785, 988, 1244, 1551, 1936, 2401, 2972, 3661, 4508, 5518, 6747, 8224, 10000, 12118, 14671, 17696, 21315, 25612, 30719, 36752, 43916, 52341, 62304, 74010, 87785

Offset

0,4

Links

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

Formula

a(n) = A240211(n) - A240209(n) for n >= 0.

a(n) + A240207(n) + A240209 = A000041(n) for n >= 0.

Example

a(6) counts these 5 partitions:  6, 51, 42, 33, 321.

Mathematica

z = 60; f[n_] := f[n] = IntegerPartitions[n];
t1 = Table[Count[f[n], p_ /; Median[p] < Count[p, Max[p]]], {n, 0, z}]  (* A240207 *)
t2 = Table[Count[f[n], p_ /; Median[p] <= Count[p, Max[p]]], {n, 0, z}] (* A240208 *)
t3 = Table[Count[f[n], p_ /; Median[p] == Count[p, Max[p]]], {n, 0, z}] (* A240209 *)
t4 = Table[Count[f[n], p_ /; Median[p] > Count[p, Max[p]]], {n, 0, z}] (* A240210 *)
t5 = Table[Count[f[n], p_ /; Median[p] >= Count[p, Max[p]]], {n, 0, z}] (* A240211 *)

Crossrefs

Cf. A240207, A240208, A240209, A240211, A000041.

Sequence in context: A111181 A267419 A076777 * A111123 A261091 A179523

Adjacent sequences: A240207 A240208 A240209 * A240211 A240212 A240213

Keyword

nonn,easy

Author

Clark Kimberling, Apr 03 2014

Status

approved