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A325857
Number of integer partitions of n such that every orderless pair of distinct parts has a different sum.
10
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 41, 55, 74, 97, 125, 165, 209, 269, 335, 428, 527, 664, 804, 1005, 1210, 1496, 1780, 2186, 2586, 3148, 3698, 4473, 5226, 6279, 7290, 8706, 10067, 11950, 13744, 16242, 18605, 21864, 24942, 29184, 33188, 38651, 43782, 50791, 57402, 66300, 74683, 86026, 96658
OFFSET
0,3
LINKS
EXAMPLE
The A000041(14) - a(14) = 10 partitions of 14 not satisfying the condition are:
(6,5,2,1)
(6,4,3,1)
(5,4,3,2)
(5,4,2,2,1)
(4,4,3,2,1)
(5,4,2,1,1,1)
(4,3,3,2,1,1)
(4,3,2,2,2,1)
(4,3,2,2,1,1,1)
(4,3,2,1,1,1,1,1)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], 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.
Sequence in context: A035988 A088669 A091580 * A023030 A246580 A212187
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 31 2019
EXTENSIONS
Terms a(31) onward from Max Alekseyev, Sep 23 2023
STATUS
approved