A241087 Number of partitions p of n into distinct parts such that max(p) = 2*(number of parts of p).

0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 2, 2, 2, 2, 2, 2, 3, 4, 4, 6, 5, 6, 6, 7, 7, 9, 10, 12, 13, 15, 16, 18, 19, 20, 23, 25, 28, 30, 35, 38, 43, 46, 51, 55, 61, 64, 72, 76, 84, 91, 101, 109, 120, 130, 142, 155, 168, 181, 196, 212, 228, 248, 266, 288, 311, 337

Offset

0,12

Links

Table of n, a(n) for n=0..66.

Example

a(15) counts these 2 partitions:  8421, 654.

Mathematica

z = 40; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
Table[Count[f[n], p_ /; Max[p] < 2*Length[p]], {n, 0, z}]  (* A241085 *)
Table[Count[f[n], p_ /; Max[p] <= 2*Length[p]], {n, 0, z}] (* A241086 *)
Table[Count[f[n], p_ /; Max[p] == 2*Length[p]], {n, 0, z}] (* A241087 *)
Table[Count[f[n], p_ /; Max[p] >= 2*Length[p]], {n, 0, z}] (* A241088 *)
Table[Count[f[n], p_ /; Max[p] > 2*Length[p]], {n, 0, z}]  (* A241089 *)

Crossrefs

Cf. A241085, A241086, A241088, A241089.

Sequence in context: A124751 A103374 A208251 * A137722 A081305 A035665

Adjacent sequences: A241084 A241085 A241086 * A241088 A241089 A241090

Keyword

nonn,easy

Author

Clark Kimberling, Apr 17 2014

Status

approved