login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A325243 Number of integer partitions of n with exactly two distinct multiplicities. 2
0, 0, 0, 0, 1, 3, 3, 9, 12, 19, 26, 39, 47, 70, 89, 115, 148, 189, 235, 294, 362, 450, 558, 669, 817, 980, 1197, 1421, 1709, 2012, 2429, 2836, 3380, 3961, 4699, 5433, 6457, 7433, 8770, 10109, 11818, 13547, 15912, 18109, 21105, 24121, 27959, 31736, 36840, 41670 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

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

The Heinz numbers of these partitions are given by A323055.

LINKS

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

EXAMPLE

The a(4) = 1 through a(9) = 19 partitions:

  (211)  (221)   (411)    (322)     (332)      (441)

         (311)   (3111)   (331)     (422)      (522)

         (2111)  (21111)  (511)     (611)      (711)

                          (2221)    (3221)     (3222)

                          (3211)    (4211)     (3321)

                          (4111)    (5111)     (4221)

                          (22111)   (22211)    (4311)

                          (31111)   (32111)    (5211)

                          (211111)  (41111)    (6111)

                                    (221111)   (22221)

                                    (311111)   (32211)

                                    (2111111)  (33111)

                                               (42111)

                                               (51111)

                                               (321111)

                                               (411111)

                                               (2211111)

                                               (3111111)

                                               (21111111)

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], Length[Union[Length/@Split[#]]]==2&]], {n, 0, 30}]

CROSSREFS

Column k = 2 of A325242. Dominated by A325267.

Cf. A008284, A062770, A071625, A098859, A116608, A244515, A323055, A325244.

Sequence in context: A117153 A045810 A166720 * A319271 A066314 A083336

Adjacent sequences:  A325240 A325241 A325242 * A325244 A325245 A325246

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 15 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 18 21:25 EDT 2019. Contains 325144 sequences. (Running on oeis4.)