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

0,5

Links

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

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A174625 A178853 A344646 * A008666 A240854 A332900

Adjacent sequences: A120638 A120639 A120640 * A120642 A120643 A120644

Keyword

nonn

Author

Reinhard Zumkeller, Aug 17 2006

Extensions

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

Status

approved