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A325244 Number of integer partitions of n with one fewer distinct multiplicities than distinct parts. 10
0, 0, 0, 1, 1, 2, 3, 4, 7, 12, 16, 21, 33, 38, 50, 75, 87, 111, 150, 185, 244, 307, 373, 461, 585, 702, 856, 1043, 1255, 1498, 1822, 2143, 2565, 3064, 3607, 4251, 5064, 5920, 6953, 8174, 9503, 11064, 12927, 14921, 17320, 19986, 23067, 26485, 30499, 34894 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

For example, (32211) has two distinct multiplicities (1, 2) and three distinct parts (1, 2, 3) so is counted under a(9).

The Heinz numbers of these partitions are given by A325259.

LINKS

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

EXAMPLE

The a(3) = 1 through a(10) = 16 partitions:

  (21)  (31)  (32)  (42)    (43)    (53)     (54)      (64)

              (41)  (51)    (52)    (62)     (63)      (73)

                    (2211)  (61)    (71)     (72)      (82)

                            (3211)  (3221)   (81)      (91)

                                    (3311)   (3321)    (3322)

                                    (4211)   (4221)    (4411)

                                    (32111)  (4311)    (5221)

                                             (5211)    (5311)

                                             (32211)   (6211)

                                             (42111)   (32221)

                                             (222111)  (33211)

                                             (321111)  (42211)

                                                       (43111)

                                                       (52111)

                                                       (421111)

                                                       (3211111)

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], Length[Union[#]]==Length[Union[Length/@Split[#]]]+1&]], {n, 0, 30}]

CROSSREFS

Cf. A008284, A071625, A090858, A098859, A116608, A117571, A127002, A325242, A325259, A325270.

Sequence in context: A223578 A073147 A249578 * A217786 A228494 A292324

Adjacent sequences:  A325241 A325242 A325243 * A325245 A325246 A325247

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 15 2019

STATUS

approved

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Last modified October 16 18:03 EDT 2019. Contains 328102 sequences. (Running on oeis4.)