cp's OEIS Frontend

A325857 Number of integer partitions of n such that every orderless pair of distinct parts has a different sum.

%I A325857 #10 Sep 23 2023 14:51:40
%S A325857 1,1,2,3,5,7,11,15,22,30,41,55,74,97,125,165,209,269,335,428,527,664,
%T A325857 804,1005,1210,1496,1780,2186,2586,3148,3698,4473,5226,6279,7290,8706,
%U A325857 10067,11950,13744,16242,18605,21864,24942,29184,33188,38651,43782,50791,57402,66300,74683,86026,96658
%N A325857 Number of integer partitions of n such that every orderless pair of distinct parts has a different sum.
%H A325857 Max Alekseyev, <a href="/A325857/b325857.txt">Table of n, a(n) for n = 0..80</a>
%e A325857 The A000041(14) - a(14) = 10 partitions of 14 not satisfying the condition are:
%e A325857   (6,5,2,1)
%e A325857   (6,4,3,1)
%e A325857   (5,4,3,2)
%e A325857   (5,4,2,2,1)
%e A325857   (4,4,3,2,1)
%e A325857   (5,4,2,1,1,1)
%e A325857   (4,3,3,2,1,1)
%e A325857   (4,3,2,2,2,1)
%e A325857   (4,3,2,2,1,1,1)
%e A325857   (4,3,2,1,1,1,1,1)
%t A325857 Table[Length[Select[IntegerPartitions[n],UnsameQ@@Plus@@@Subsets[Union[#],{2}]&]],{n,0,30}]
%Y A325857 The subset case is A196723.
%Y A325857 The maximal case is A325878.
%Y A325857 The integer partition case is A325857.
%Y A325857 The strict integer partition case is A325877.
%Y A325857 Heinz numbers of the counterexamples are given by A325991.
%Y A325857 Cf. A002033, A103300, A108917, A143823, A196724, A325853, A325855, A325858, A325859, A325862.
%K A325857 nonn
%O A325857 0,3
%A A325857 _Gus Wiseman_, May 31 2019
%E A325857 Terms a(31) onward from _Max Alekseyev_, Sep 23 2023