A240207 Number of partitions p of n such that median(p) < multiplicity(max(p)).

0, 0, 1, 1, 1, 1, 3, 3, 4, 5, 6, 8, 11, 14, 18, 24, 27, 35, 41, 52, 65, 79, 96, 122, 145, 177, 213, 256, 307, 368, 434, 524, 623, 741, 876, 1049, 1230, 1458, 1714, 2019, 2362, 2778, 3234, 3792, 4412, 5148, 5980, 6970, 8069, 9372, 10846, 12559, 14491, 16754

Offset

0,7

Links

Table of n, a(n) for n=0..53.

Formula

a(n) = A240209(n) - A240208(n) for n >= 0.

a(n) + A240209(n) + A240210(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_ /; 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. A240208, A240209, A240210, A240211, A000041.

Sequence in context: A011977 A104803 A104804 * A347286 A144489 A239640

Adjacent sequences: A240204 A240205 A240206 * A240208 A240209 A240210

Keyword

nonn,easy

Author

Clark Kimberling, Apr 03 2014

Status

approved