A240212 Number of partitions p of n such that median(p) < multiplicity(min(p)).

0, 0, 1, 1, 2, 3, 6, 7, 10, 14, 19, 26, 37, 48, 65, 87, 115, 150, 194, 250, 322, 407, 518, 653, 823, 1029, 1287, 1598, 1984, 2449, 3021, 3706, 4540, 5540, 6752, 8197, 9933, 12004, 14482, 17421, 20924, 25070, 29992, 35797, 42661, 50735, 60254, 71421, 84536

Offset

0,5

Links

Table of n, a(n) for n=0..48.

Formula

a(n) = A240213(n) - A240214(n) for n >= 0.

a(n) + A240214(n) + A240216(n) = A000041(n) for n >= 0.

Example

a(8) counts these 10 partitions:  611, 5111, 4211, 41111, 32111, 311111, 2222, 221111, 2111111, 11111111.

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. A240213, A240214, A240215, A240216, A000041.

Sequence in context: A351554 A002038 A032501 * A333551 A093677 A343604

Adjacent sequences: A240209 A240210 A240211 * A240213 A240214 A240215

Keyword

nonn,easy

Author

Clark Kimberling, Apr 04 2014

Status

approved