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A325333 Number of integer partitions of n whose multiplicities all appear the same number of times. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..49.

EXAMPLE

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).

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A260904 A245808 A252797 * A036608 A309097 A309098

Adjacent sequences:  A325330 A325331 A325332 * A325334 A325335 A325336

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 01 2019

STATUS

approved

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Last modified August 10 14:50 EDT 2020. Contains 336381 sequences. (Running on oeis4.)