A240209 Number of partitions p of n such that median(p) = multiplicity(max(p)).

0, 1, 0, 0, 2, 3, 3, 4, 7, 9, 13, 18, 24, 30, 41, 50, 70, 85, 117, 140, 182, 225, 287, 348, 442, 537, 672, 818, 1010, 1225, 1509, 1810, 2208, 2655, 3210, 3834, 4629, 5508, 6605, 7851, 9364, 11086, 13188, 15553, 18422, 21682, 25568, 29999, 35285, 41279, 48378

Offset

0,5

Links

Table of n, a(n) for n=0..50.

Formula

a(n) = A240208(n) + A240207(n) for n >= 0.

a(n) + A240207(n) + A240210 = A000041(n) for n >= 0.

Example

a(6) counts these 3 partitions:  411, 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, A240210, A240211, A000041.

Sequence in context: A329301 A327134 A140514 * A047079 A207624 A203990

Adjacent sequences: A240206 A240207 A240208 * A240210 A240211 A240212

Keyword

nonn,easy

Author

Clark Kimberling, Apr 03 2014

Status

approved