A325333 - OEIS

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

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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