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%I #10 Mar 14 2021 15:53:32
%S 1,1,1,2,2,3,4,5,6,8,9,12,14,18,19,26,28,36,37,50,52,67,68,89,94,115,
%T 121,151,160,195,200,247,265,312,329,386,418,487,519,600,640,742,792,
%U 901,978,1088,1185,1331,1453,1605,1729,1925,2101,2311,2524,2741,3000
%N Number of strict integer partitions of n such that every orderless pair of distinct parts has a different sum.
%C The non-strict case is A325857.
%H Fausto A. C. Cariboni, <a href="/A325877/b325877.txt">Table of n, a(n) for n = 0..450</a>
%e The a(1) = 1 through a(10) = 9 partitions (A = 10):
%e (1) (2) (3) (4) (5) (6) (7) (8) (9) (A)
%e (21) (31) (32) (42) (43) (53) (54) (64)
%e (41) (51) (52) (62) (63) (73)
%e (321) (61) (71) (72) (82)
%e (421) (431) (81) (91)
%e (521) (432) (532)
%e (531) (541)
%e (621) (631)
%e (721)
%t Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&UnsameQ@@Plus@@@Subsets[Union[#],{2}]&]],{n,0,30}]
%Y The subset case is A196723.
%Y The maximal case is A325878.
%Y The integer partition case is A325857.
%Y The strict integer partition case is A325877.
%Y Heinz numbers of the counterexamples are given by A325991.
%Y Cf. A002033, A108917, A143823, A275972.
%Y Cf. A325854, A325855, A325858, A325862, A325864, A325876, A325879.
%K nonn
%O 0,4
%A _Gus Wiseman_, Jun 02 2019