A237751 Number of partitions of n such that 2*(greatest part) < (number of parts).

0, 0, 1, 1, 1, 2, 3, 4, 6, 8, 10, 14, 18, 24, 32, 41, 52, 67, 85, 107, 135, 169, 210, 263, 324, 400, 493, 604, 736, 899, 1091, 1322, 1599, 1929, 2319, 2787, 3336, 3989, 4760, 5669, 6734, 7994, 9465, 11192, 13211, 15571, 18319, 21531, 25257, 29594, 34626

Offset

1,6

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.

Links

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

Formula

a(n) = A000041(n) - A237755(n).

Example

a(6) = 2 counts these partitions:  21111, 111111.

Mathematica

z = 55; Table[Count[IntegerPartitions[n], p_ /; 2 Max[p] < Length[p]], {n, z}]

Crossrefs

Cf. A064173, A237752-A237757, A000041.

Sequence in context: A260183 A134157 A274194 * A045476 A368381 A323360

Adjacent sequences: A237748 A237749 A237750 * A237752 A237753 A237754

Keyword

nonn,easy

Author

Clark Kimberling, Feb 13 2014

Status

approved