A325341 Number of partitions p of n such that min(p) <= (number of parts of p) < max(p).

0, 0, 0, 1, 2, 3, 4, 7, 10, 15, 21, 29, 39, 54, 71, 95, 124, 163, 209, 271, 344, 440, 554, 700, 874, 1095, 1357, 1685, 2076, 2559, 3132, 3837, 4671, 5687, 6889, 8343, 10058, 12123, 14552, 17459, 20875, 24941, 29706, 35358, 41966, 49768, 58875, 69587, 82061

Offset: 1

Author

Clark Kimberling, Apr 21 2019

Keywords

• nonn

Examples

			a(7) counts these 4 partitions: {6,1}, {5,2}, {5,1,1}, {4,2,1}.
		

Links

• Jason Yuen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000041, A003106, A064174, A325340, A325342, A325343.

Programs

Mathematica

Table[Count[IntegerPartitions[n], q_ /; Min[q] <= Length[q] < Max[q]], {n, 60}]

Formula

a(n) = A000041(n) - A003106(n) - A064174(n). - Jason Yuen, Dec 17 2024