A325343 Number of partitions p of n such that min(p) <= (number of parts of p) <= max(p).

1, 0, 1, 2, 3, 4, 7, 9, 14, 19, 27, 36, 50, 65, 87, 114, 149, 192, 249, 316, 404, 510, 643, 805, 1008, 1251, 1553, 1917, 2361, 2895, 3546, 4322, 5262, 6383, 7728, 9330, 11245, 13512, 16213, 19405, 23186, 27643, 32907, 39089, 46366, 54894, 64893, 76584, 90256

Offset: 1

Author

Clark Kimberling, Apr 21 2019

Keywords

• nonn

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000041, A003106, A064173, A325340, A325341, A325342.

Programs

Mathematica

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

Formula

a(n) = A000041(n) - A003106(n) - A064173(n) for n > 0. - Jason Yuen, Dec 15 2024