cp's OEIS Frontend

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

%I A120641 #12 Feb 16 2025 08:33:01
%S A120641 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,
%T A120641 101,116,132,151,170,194,222,247,281,318,356,399,452,509,567,635,709,
%U A120641 794,885,983,1094,1222,1358,1504,1671,1854,2050,2264,2505,2771,3060,3370
%N A120641 Number of partitions of n into distinct double-free parts.
%H A120641 Alois P. Heinz, <a href="/A120641/b120641.txt">Table of n, a(n) for n = 0..400</a>
%H A120641 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Double-FreeSet.html">Double-Free Set</a>
%e A120641 a(10) = #{10, 9+1, 8+2, 7+3, 6+4, 5+4+1, 5+3+2} = 7;
%e A120641 a(11) = #{11, 10+1, 9+2, 8+3, 7+4, 7+3+1, 6+5, 6+4+1} = 8.
%t A120641 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&Intersection[#,2*#]=={}&]],{n,30}] (* _Gus Wiseman_, Jan 07 2019 *)
%Y A120641 Cf. A000009, A050291, A101417, A303362, A320340, A323092, A323093, A323094.
%K A120641 nonn
%O A120641 0,5
%A A120641 _Reinhard Zumkeller_, Aug 17 2006
%E A120641 a(0)=1 prepended by _Alois P. Heinz_, Jan 16 2019