A320226 Number of integer partitions of n whose non-1 parts are all equal.

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

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: A234718 A341158 A294849 * A290564 A167803 A367402

Adjacent sequences: A320223 A320224 A320225 * A320227 A320228 A320229

Keyword

nonn

Author

Gus Wiseman, Oct 07 2018

Status

approved