A120641 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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