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

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, 121, 151, 160, 195, 200, 247, 265, 312, 329, 386, 418, 487, 519, 600, 640, 742, 792, 901, 978, 1088, 1185, 1331, 1453, 1605, 1729, 1925, 2101, 2311, 2524, 2741, 3000

Offset: 0

Author

Gus Wiseman, Jun 02 2019

Keywords

• nonn

Comments

The non-strict case is A325857.

Examples

			The a(1) = 1 through a(10) = 9 partitions (A = 10):
  (1)  (2)  (3)   (4)   (5)   (6)    (7)    (8)    (9)    (A)
            (21)  (31)  (32)  (42)   (43)   (53)   (54)   (64)
                        (41)  (51)   (52)   (62)   (63)   (73)
                              (321)  (61)   (71)   (72)   (82)
                                     (421)  (431)  (81)   (91)
                                            (521)  (432)  (532)
                                                   (531)  (541)
                                                   (621)  (631)
                                                          (721)
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..450

Crossrefs

The subset case is A196723.

The maximal case is A325878.

The integer partition case is A325857.

The strict integer partition case is A325877.

Heinz numbers of the counterexamples are given by A325991.

Cf. A002033, A108917, A143823, A275972.

Cf. A325854, A325855, A325858, A325862, A325864, A325876, A325879.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&UnsameQ@@Plus@@@Subsets[Union[#],{2}]&]],{n,0,30}]