login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A325858 Number of Golomb partitions of n. 20
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..49.

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.

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

Sequence in context: A001522 A054405 A155167 * A237269 A116634 A035960

Adjacent sequences:  A325855 A325856 A325857 * A325859 A325860 A325861

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 02 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 18 11:39 EDT 2019. Contains 325139 sequences. (Running on oeis4.)