A241091 Number of partitions p of n into distinct parts such that max(p) <= 1 + 2*(number of parts of p).

0, 1, 1, 2, 1, 2, 3, 3, 3, 4, 5, 5, 7, 7, 9, 10, 11, 12, 15, 16, 19, 22, 24, 27, 30, 34, 37, 43, 47, 53, 59, 66, 72, 82, 88, 99, 109, 120, 131, 146, 160, 176, 194, 212, 233, 256, 279, 304, 334, 362, 396, 431, 471, 510, 558, 604, 659, 714, 776, 839, 913, 985

Offset

0,4

Links

Table of n, a(n) for n=0..61.

Formula

a(n) = A241086(n) + A241092(n) for n >= 0.

Example

a(12) counts these 5 partitions:  741, 732, 651, 642, 6321, 543, 5421.

Mathematica

z = 30; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
 Table[Count[f[n], p_ /; Max[p] < 1 + 2*Length[p]], {n, 0, z}] (*A241086*)
 Table[Count[f[n], p_ /; Max[p] <= 1 + 2*Length[p]], {n, 0, z}](*A241091*)
 Table[Count[f[n], p_ /; Max[p] == 1 + 2*Length[p]], {n, 0, z}](*A241092*)
 Table[Count[f[n], p_ /; Max[p] >= 1 + 2*Length[p]], {n, 0, z}](*A241089*)
 Table[Count[f[n], p_ /; Max[p] > 1 + 2*Length[p]], {n, 0, z}] (*A241093*)

Crossrefs

Cf. A241086, A241092, A241093.

Sequence in context: A240873 A208882 A186519 * A137719 A029165 A035431

Adjacent sequences: A241088 A241089 A241090 * A241092 A241093 A241094

Keyword

nonn,easy

Author

Clark Kimberling, Apr 18 2014

Status

approved