A323092 Number of double-free integer partitions of n.

1, 1, 2, 2, 4, 5, 7, 10, 14, 17, 24, 30, 40, 50, 66, 81, 104, 128, 161, 197, 246, 300, 369, 446, 546, 656, 796, 952, 1148, 1366, 1637, 1940, 2311, 2730, 3234, 3806, 4489, 5262, 6181, 7225, 8454, 9846, 11484, 13335, 15499, 17948, 20796, 24017, 27751, 31970, 36837

Offset

0,3

Comments

An integer partition is double-free if no part is twice any other part.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..400

Eric Weisstein's World of Mathematics, Double-Free Set

Example

The a(1) = 1 through a(8) = 14 double-free integer partitions:
  (1)  (2)   (3)    (4)     (5)      (6)       (7)        (8)
       (11)  (111)  (22)    (32)     (33)      (43)       (44)
                    (31)    (41)     (51)      (52)       (53)
                    (1111)  (311)    (222)     (61)       (62)
                            (11111)  (411)     (322)      (71)
                                     (3111)    (331)      (332)
                                     (111111)  (511)      (431)
                                               (4111)     (611)
                                               (31111)    (2222)
                                               (1111111)  (3311)
                                                          (5111)
                                                          (41111)
                                                          (311111)
                                                          (11111111)

Mathematica

Table[Length[Select[IntegerPartitions[n], Intersection[#, 2*#]=={}&]], {n, 30}]

Crossrefs

Cf. A018819, A051424, A101417, A120641, A276431, A305148, A323093, A323094.

Sequence in context: A363260 A195012 A333192 * A238594 A350837 A239945

Adjacent sequences: A323089 A323090 A323091 * A323093 A323094 A323095

Keyword

nonn

Author

Gus Wiseman, Jan 04 2019

Status

approved