OFFSET
0,3
COMMENTS
We define a Golomb partition of n to be an integer partition of n such that every pair of distinct parts has a different difference.
Also the number of integer partitions of n such that every orderless pair of (not necessarily distinct) parts has a different sum.
The strict case is A325876.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..250
EXAMPLE
The a(1) = 1 through a(7) = 14 partitions:
(1) (2) (3) (4) (5) (6) (7)
(11) (21) (22) (32) (33) (43)
(111) (31) (41) (42) (52)
(211) (221) (51) (61)
(1111) (311) (222) (322)
(2111) (411) (331)
(11111) (2211) (421)
(3111) (511)
(21111) (2221)
(111111) (4111)
(22111)
(31111)
(211111)
(1111111)
The A000041(9) - a(9) = 5 non-Golomb partitions of 9 are: (531), (432), (3321), (32211), (321111).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@Subtract@@@Subsets[Union[#], {2}]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 02 2019
STATUS
approved