A325333 Number of integer partitions of n whose multiplicities all appear the same number of times.

1, 1, 2, 3, 5, 7, 11, 14, 19, 23, 32, 39, 50, 63, 82, 96, 125, 152, 186, 226, 271, 326, 392, 473, 552, 663, 771, 918, 1065, 1261, 1448, 1710, 1953, 2283, 2608, 3062, 3455, 4013, 4552, 5271, 5974, 6884, 7774, 8937, 10065, 11570, 12953, 14838, 16710, 18979

Offset: 0

Author

Gus Wiseman, May 01 2019

Keywords

• nonn

Examples

			The a(0) = 1 through a(7) = 14 partitions:
  ()  (1)  (2)   (3)    (4)     (5)      (6)       (7)
           (11)  (21)   (22)    (32)     (33)      (43)
                 (111)  (31)    (41)     (42)      (52)
                        (211)   (221)    (51)      (61)
                        (1111)  (311)    (222)     (322)
                                (2111)   (321)     (331)
                                (11111)  (411)     (421)
                                         (2211)    (511)
                                         (3111)    (2221)
                                         (21111)   (4111)
                                         (111111)  (22111)
                                                   (31111)
                                                   (211111)
                                                   (1111111)
For example, the partition (4,3,3,3,2,2,2,1) has multiplicities (1,3,3,1), and since both multiplicities 1 and 3 appear twice, (4,3,3,3,2,2,2,1) is counted under a(20).
		

Crossrefs

Cf. A000041, A007862, A047966, A049988, A098859, A323022, A325329, A325369.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n],SameQ@@Length/@Split[Sort[Length/@Split[#]]]&]],{n,0,30}]