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A325877 Number of strict integer partitions of n such that every orderless pair of distinct parts has a different sum.

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