A240312 Number of partitions p of n such that (maximal multiplicity of the parts of p) = (maximal part of p).

1, 1, 0, 0, 2, 1, 2, 0, 2, 3, 5, 5, 9, 7, 11, 11, 18, 15, 28, 27, 41, 43, 62, 64, 91, 96, 127, 140, 184, 200, 260, 287, 365, 410, 511, 573, 717, 803, 985, 1120, 1359, 1538, 1859, 2106, 2522, 2870, 3407, 3872, 4586, 5207, 6128, 6976, 8167, 9284, 10844, 12321

Offset

0,5

Links

Table of n, a(n) for n=0..55.

Formula

a(n) = A240311(n) - A240310(n) for n >= 0.

a(n) + A240310(n) + A240314(n) = A000041(n) for n >= 0.

Example

a(6) counts these 2 partitions:  3111, 2211.

Mathematica

z = 60; f[n_] := f[n] = IntegerPartitions[n]; m[p_] := Max[Map[Length, Split[p]]]  (* maximal multiplicity *)
Table[Count[f[n], p_ /; m[p] < Max[p]], {n, 0, z}]  (* A240310 *)
Table[Count[f[n], p_ /; m[p] <= Max[p]], {n, 0, z}] (* A240311 *)
Table[Count[f[n], p_ /; m[p] == Max[p]], {n, 0, z}] (* A240312 *)
Table[Count[f[n], p_ /; m[p] >= Max[p]], {n, 0, z}] (* A240313 *)
Table[Count[f[n], p_ /; m[p] > Max[p]], {n, 0, z}]  (* A240314 *)

Crossrefs

Cf. A240310, A240311, A240313, A240314, A000041.

Sequence in context: A137423 A127471 A309044 * A339898 A273163 A276695

Adjacent sequences: A240309 A240310 A240311 * A240313 A240314 A240315

Keyword

nonn,easy

Author

Clark Kimberling, Apr 05 2014

Status

approved