login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A320226 Number of integer partitions of n whose non-1 parts are all equal. 5
1, 1, 2, 3, 5, 6, 9, 10, 13, 15, 18, 19, 24, 25, 28, 31, 35, 36, 41, 42, 47, 50, 53, 54, 61, 63, 66, 69, 74, 75, 82, 83, 88, 91, 94, 97, 105, 106, 109, 112, 119, 120, 127, 128, 133, 138, 141, 142, 151, 153, 158, 161, 166, 167, 174, 177, 184, 187, 190, 191, 202 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..60.

Jonathan Bloom, Nathan McNew, Counting pattern-avoiding integer partitions, arXiv:1908.03953 [math.CO], 2019.

FORMULA

a(n > 1) = A002541(n - 1) + 1.

EXAMPLE

The integer partitions whose non-1 parts are all equal:

  (1)  (2)   (3)    (4)     (5)      (6)       (7)        (8)

       (11)  (21)   (22)    (41)     (33)      (61)       (44)

             (111)  (31)    (221)    (51)      (331)      (71)

                    (211)   (311)    (222)     (511)      (611)

                    (1111)  (2111)   (411)     (2221)     (2222)

                            (11111)  (2211)    (4111)     (3311)

                                     (3111)    (22111)    (5111)

                                     (21111)   (31111)    (22211)

                                     (111111)  (211111)   (41111)

                                               (1111111)  (221111)

                                                          (311111)

                                                          (2111111)

                                                          (11111111)

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], SameQ@@DeleteCases[#, 1]&]], {n, 30}]

CROSSREFS

Cf. A002541, A003238, A070776, A126656, A316782, A317712, A320224, A320225.

Sequence in context: A029455 A234718 A294849 * A290564 A167803 A092213

Adjacent sequences:  A320223 A320224 A320225 * A320227 A320228 A320229

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 07 2018

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 8 17:40 EDT 2020. Contains 335524 sequences. (Running on oeis4.)