A240216 Number of partitions p of n such that median(p) >= multiplicity(min(p)).

0, 1, 1, 2, 3, 4, 5, 8, 12, 16, 23, 30, 40, 53, 70, 89, 116, 147, 191, 240, 305, 385, 484, 602, 752, 929, 1149, 1412, 1734, 2116, 2583, 3136, 3809, 4603, 5558, 6686, 8044, 9633, 11533, 13764, 16414, 19513, 23182, 27464, 32514, 38399, 45304, 53333, 62737

Offset

0,4

Links

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

Formula

a(n) = A240215(n) + A240215(n) for n >= 0.

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

Example

a(6) counts these 12 partitions:  8, 71, 62, 53, 521, 44, 431, 422, 332, 3311, 321, 22211.

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, A240215, A000041.

Sequence in context: A254328 A094087 A225132 * A017821 A113439 A274112

Adjacent sequences: A240213 A240214 A240215 * A240217 A240218 A240219

Keyword

nonn,easy

Author

Clark Kimberling, Apr 04 2014

Status

approved