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Number of double-free integer partitions of n.
47

%I #7 Jan 22 2019 18:28:51

%S 1,1,2,2,4,5,7,10,14,17,24,30,40,50,66,81,104,128,161,197,246,300,369,

%T 446,546,656,796,952,1148,1366,1637,1940,2311,2730,3234,3806,4489,

%U 5262,6181,7225,8454,9846,11484,13335,15499,17948,20796,24017,27751,31970,36837

%N Number of double-free integer partitions of n.

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

%H Alois P. Heinz, <a href="/A323092/b323092.txt">Table of n, a(n) for n = 0..400</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Double-FreeSet.html">Double-Free Set</a>

%e The a(1) = 1 through a(8) = 14 double-free integer partitions:

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

%e (11) (111) (22) (32) (33) (43) (44)

%e (31) (41) (51) (52) (53)

%e (1111) (311) (222) (61) (62)

%e (11111) (411) (322) (71)

%e (3111) (331) (332)

%e (111111) (511) (431)

%e (4111) (611)

%e (31111) (2222)

%e (1111111) (3311)

%e (5111)

%e (41111)

%e (311111)

%e (11111111)

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

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

%K nonn

%O 0,3

%A _Gus Wiseman_, Jan 04 2019