A120641 Number of partitions of n into distinct double-free parts.

1, 1, 1, 1, 2, 3, 2, 4, 5, 5, 7, 8, 10, 12, 14, 17, 20, 24, 26, 31, 38, 45, 50, 57, 68, 77, 88, 101, 116, 132, 151, 170, 194, 222, 247, 281, 318, 356, 399, 452, 509, 567, 635, 709, 794, 885, 983, 1094, 1222, 1358, 1504, 1671, 1854, 2050, 2264, 2505, 2771, 3060, 3370

Offset: 0

Author

Reinhard Zumkeller, Aug 17 2006

Keywords

• nonn

Examples

			a(10) = #{10, 9+1, 8+2, 7+3, 6+4, 5+4+1, 5+3+2} = 7;
a(11) = #{11, 10+1, 9+2, 8+3, 7+4, 7+3+1, 6+5, 6+4+1} = 8.
		

Links

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

Crossrefs

Cf. A000009, A050291, A101417, A303362, A320340, A323092, A323093, A323094.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&Intersection[#,2*#]=={}&]],{n,30}] (* Gus Wiseman, Jan 07 2019 *)

Extensions

a(0)=1 prepended by Alois P. Heinz, Jan 16 2019