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A325858 Number of Golomb partitions of n. 20

%I

%S 1,1,2,3,5,7,10,14,20,25,36,47,59,78,99,122,155,195,232,295,355,432,

%T 522,641,749,919,1076,1283,1506,1802,2067,2470,2835,3322,3815,4496,

%U 5070,5959,6736,7807,8849,10266,11499,13326,14928,17140,19193,22037,24519,28106

%N Number of Golomb partitions of n.

%C 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 Also the number of integer partitions of n such that every orderless pair of (not necessarily distinct) parts has a different sum.

%C The strict case is A325876.

%e The a(1) = 1 through a(7) = 14 partitions:

%e (1) (2) (3) (4) (5) (6) (7)

%e (11) (21) (22) (32) (33) (43)

%e (111) (31) (41) (42) (52)

%e (211) (221) (51) (61)

%e (1111) (311) (222) (322)

%e (2111) (411) (331)

%e (11111) (2211) (421)

%e (3111) (511)

%e (21111) (2221)

%e (111111) (4111)

%e (22111)

%e (31111)

%e (211111)

%e (1111111)

%e The A000041(9) - a(9) = 5 non-Golomb partitions of 9 are: (531), (432), (3321), (32211), (321111).

%t Table[Length[Select[IntegerPartitions[n],UnsameQ@@Subtract@@@Subsets[Union[#],{2}]&]],{n,0,30}]

%Y The subset case is A143823.

%Y The maximal case is A325879.

%Y The integer partition case is A325858.

%Y The strict integer partition case is A325876.

%Y Heinz numbers of the counterexamples are given by A325992.

%Y Cf. A002033, A108917, A325325, A325853, A325856, A325868.

%K nonn

%O 0,3

%A _Gus Wiseman_, Jun 02 2019

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Last modified August 18 20:02 EDT 2019. Contains 326109 sequences. (Running on oeis4.)