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A325858 Number of Golomb partitions of n.

%I A325858 #9 Mar 17 2021 20:12:23
%S A325858 1,1,2,3,5,7,10,14,20,25,36,47,59,78,99,122,155,195,232,295,355,432,
%T A325858 522,641,749,919,1076,1283,1506,1802,2067,2470,2835,3322,3815,4496,
%U A325858 5070,5959,6736,7807,8849,10266,11499,13326,14928,17140,19193,22037,24519,28106
%N A325858 Number of Golomb partitions of n.
%C A325858 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.
%C A325858 Also the number of integer partitions of n such that every orderless pair of (not necessarily distinct) parts has a different sum.
%C A325858 The strict case is A325876.
%H A325858 Fausto A. C. Cariboni, <a href="/A325858/b325858.txt">Table of n, a(n) for n = 0..250</a>
%e A325858 The a(1) = 1 through a(7) = 14 partitions:
%e A325858   (1)  (2)   (3)    (4)     (5)      (6)       (7)
%e A325858        (11)  (21)   (22)    (32)     (33)      (43)
%e A325858              (111)  (31)    (41)     (42)      (52)
%e A325858                     (211)   (221)    (51)      (61)
%e A325858                     (1111)  (311)    (222)     (322)
%e A325858                             (2111)   (411)     (331)
%e A325858                             (11111)  (2211)    (421)
%e A325858                                      (3111)    (511)
%e A325858                                      (21111)   (2221)
%e A325858                                      (111111)  (4111)
%e A325858                                                (22111)
%e A325858                                                (31111)
%e A325858                                                (211111)
%e A325858                                                (1111111)
%e A325858 The A000041(9) - a(9) = 5 non-Golomb partitions of 9 are: (531), (432), (3321), (32211), (321111).
%t A325858 Table[Length[Select[IntegerPartitions[n],UnsameQ@@Subtract@@@Subsets[Union[#],{2}]&]],{n,0,30}]
%Y A325858 The subset case is A143823.
%Y A325858 The maximal case is A325879.
%Y A325858 The integer partition case is A325858.
%Y A325858 The strict integer partition case is A325876.
%Y A325858 Heinz numbers of the counterexamples are given by A325992.
%Y A325858 Cf. A002033, A108917, A325325, A325853, A325856, A325868.
%K A325858 nonn
%O A325858 0,3
%A A325858 _Gus Wiseman_, Jun 02 2019