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

Author

Clark Kimberling, Feb 13 2014

Keywords

• nonn
• easy

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.

Examples

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

Links

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

Crossrefs

Cf. A064173, A237752-A237757, A000041.

Programs

Mathematica

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

Formula

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