A325342 Number of partitions p of n such that min(p) < (number of parts of p) <= max(p).

0, 0, 1, 1, 2, 3, 6, 8, 12, 17, 24, 33, 46, 61, 82, 108, 142, 184, 239, 305, 391, 495, 626, 786, 985, 1226, 1524, 1884, 2323, 2853, 3497, 4268, 5200, 6314, 7650, 9243, 11146, 13403, 16090, 19268, 23032, 27473, 32716, 38878, 46130, 54633, 64603, 76264, 89899

Offset: 1

Author

Clark Kimberling, Apr 21 2019

Keywords

• nonn

Examples

			a(7) counts these 6 partitions: {6,1}, {5,1,1}, {4,2,1}, {4,1,1,1}, {3,3,1}, {3,2,2}.
		

Links

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

Crossrefs

Cf. A000041, A003114, A064173, A325340, A325341, A325343.

Programs

Mathematica

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

Formula

a(n) = A000041(n) - A003114(n) - A064173(n). - Jason Yuen, Dec 17 2024