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A325858
Number of Golomb partitions of n.
21
1, 1, 2, 3, 5, 7, 10, 14, 20, 25, 36, 47, 59, 78, 99, 122, 155, 195, 232, 295, 355, 432, 522, 641, 749, 919, 1076, 1283, 1506, 1802, 2067, 2470, 2835, 3322, 3815, 4496, 5070, 5959, 6736, 7807, 8849, 10266, 11499, 13326, 14928, 17140, 19193, 22037, 24519, 28106
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
The subset case is A143823.
The maximal case is A325879.
The integer partition case is A325858.
The strict integer partition case is A325876.
Heinz numbers of the counterexamples are given by A325992.
Sequence in context: A001522 A054405 A155167 * A237269 A116634 A035960
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 02 2019
STATUS
approved