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

Author

Gus Wiseman, Oct 07 2018

Keywords

• nonn

Examples

			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)
		

Links

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

Crossrefs

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

Programs

Mathematica

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

Formula

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