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

Author

Gus Wiseman, Jan 04 2019

Keywords

• nonn

Comments

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

Examples

			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)
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..400
• Eric Weisstein's World of Mathematics, Double-Free Set

Crossrefs

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

Programs

Mathematica

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