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

0,4

Comments

The non-strict case is A325857.

Links

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

Example

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)

Mathematica

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

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.

Sequence in context: A069911 A185225 A027196 * A100928 A240671 A034140

Adjacent sequences: A325874 A325875 A325876 * A325878 A325879 A325880

Keyword

nonn

Author

Gus Wiseman, Jun 02 2019

Status

approved