A237752 Number of partitions of n such that 2*(greatest part) <= (number of parts).

0, 1, 1, 1, 2, 3, 4, 6, 7, 10, 13, 18, 23, 31, 39, 50, 64, 82, 102, 130, 162, 203, 252, 313, 384, 475, 580, 710, 864, 1053, 1273, 1544, 1859, 2240, 2688, 3224, 3851, 4602, 5476, 6514, 7727, 9160, 10826, 12791, 15072, 17747, 20853, 24481, 28679, 33577, 39231

Offset

1,5

Comments

Also, the number of partitions of n such that (greatest part) >= 2*(number of parts); hence, the number of partitions of n such that (rank + greatest part) <= 0.

Also, the number of partitions p of n such that max(max(p), 2*(number of parts of p)) is a part of p.

Links

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Formula

a(n) = A000041(n) - A237754(n).

Example

The partitions of 6 that do not qualify are 22311, 21111, 111111, so that a(6) = 11 - 3 = 8.

Mathematica

z = 50; Table[Count[IntegerPartitions[n], p_ /; 2 Max[p] <= Length[p]], {n, z}]
(* also *)
Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, Max[Max[p], 2*Length[p]]]], {n, 50}]

Crossrefs

Cf. A064173, A237751, A237753-A237757, A000041.

Sequence in context: A199118 A035941 A039854 * A032480 A226137 A355393

Adjacent sequences: A237749 A237750 A237751 * A237753 A237754 A237755

Keyword

nonn,easy

Author

Clark Kimberling, Feb 13 2014

Status

approved