A240310 Number of partitions p of n such that (maximal multiplicity of the parts of p) < (maximal part of p).

0, 0, 1, 2, 2, 4, 6, 10, 14, 19, 27, 37, 50, 69, 92, 123, 161, 213, 273, 355, 453, 580, 734, 931, 1168, 1468, 1830, 2279, 2821, 3490, 4292, 5275, 6450, 7878, 9584, 11645, 14091, 17039, 20529, 24703, 29640, 35520, 42447, 50669, 60329, 71743, 85131, 100892

Offset

0,4

Links

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

Formula

a(n) = A240311(n) - A240312(n) for n >= 0.

a(n) + A240312(n) + A240314(n) = A000041(n) for n >= 0.

Example

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

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. A240311, A240312, A240313, A240314, A000041.

Sequence in context: A236634 A034406 A098330 * A083848 A330644 A278297

Adjacent sequences: A240307 A240308 A240309 * A240311 A240312 A240313

Keyword

nonn,easy

Author

Clark Kimberling, Apr 05 2014

Status

approved