A240211 Number of partitions p of n such that median(p) >= multiplicity(max(p)).

0, 1, 1, 2, 4, 6, 8, 12, 18, 25, 36, 48, 66, 87, 117, 152, 204, 262, 344, 438, 562, 713, 906, 1133, 1430, 1781, 2223, 2754, 3411, 4197, 5170, 6318, 7726, 9402, 11434, 13834, 16747, 20179, 24301, 29166, 34976, 41805, 49940, 59469, 70763, 83986, 99578, 117784

Offset

0,4

Links

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

Formula

a(n) = A240209(n) + A240210(n) for n >= 0.

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

Example

a(6) counts these 8 partitions:  6, 51, 42, 411, 33, 321, 3111, 21111.

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, A240210, A000041.

Sequence in context: A292854 A330813 A015897 * A050597 A288603 A324939

Adjacent sequences: A240208 A240209 A240210 * A240212 A240213 A240214

Keyword

nonn,easy

Author

Clark Kimberling, Apr 03 2014

Status

approved