OFFSET
0,4
COMMENTS
We define a Golomb partition of n to be an integer partition of n such that every ordered pair of distinct parts has a different difference.
Also the number of strict integer partitions of n such that every orderless pair of (not necessarily distinct) parts has a different sum.
The non-strict case is A325858.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..500
EXAMPLE
The a(2) = 1 through a(11) = 11 partitions (A = 10, B = 11):
(2) (3) (4) (5) (6) (7) (8) (9) (A) (B)
(21) (31) (32) (42) (43) (53) (54) (64) (65)
(41) (51) (52) (62) (63) (73) (74)
(61) (71) (72) (82) (83)
(421) (431) (81) (91) (92)
(521) (621) (532) (A1)
(541) (542)
(631) (632)
(721) (641)
(731)
(821)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&UnsameQ@@Subtract@@@Subsets[Union[#], {2}]&]], {n, 0, 30}]
PROG
(Python)
from collections import Counter
from itertools import combinations
from sympy.utilities.iterables import partitions
def A325876(n): return sum(1 for p in partitions(n) if max(list(Counter(abs(d[0]-d[1]) for d in combinations(list(Counter(p).elements()), 2)).values()), default=1)==1)-(n&1^1) if n else 1 # Chai Wah Wu, Sep 17 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 02 2019
STATUS
approved