A240208 Number of partitions p of n such that median(p) <= multiplicity(max(p)).

0, 1, 1, 1, 3, 4, 6, 7, 11, 14, 19, 26, 35, 44, 59, 74, 97, 120, 158, 192, 247, 304, 383, 470, 587, 714, 885, 1074, 1317, 1593, 1943, 2334, 2831, 3396, 4086, 4883, 5859, 6966, 8319, 9870, 11726, 13864, 16422, 19345, 22834, 26830, 31548, 36969, 43354, 50651

Offset

0,5

Links

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

Formula

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

a(n) + A240210(n) = A000041(n) for n >= 0.

Example

a(6) counts these 6 partitions:  411, 3111, 222, 2211, 21111, 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. A240207, A240209, A240210, A240211, A000041.

Sequence in context: A075434 A085253 A207525 * A349555 A073906 A108797

Adjacent sequences: A240205 A240206 A240207 * A240209 A240210 A240211

Keyword

nonn,easy

Author

Clark Kimberling, Apr 03 2014

Status

approved