login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A325862 Number of integer partitions of n such that every set of distinct parts has a different sum. 9
1, 1, 2, 3, 5, 7, 10, 14, 19, 26, 34, 46, 58, 77, 93, 122, 146, 188, 217, 282, 327, 410, 470, 596, 673, 848, 947, 1178, 1325, 1629, 1798, 2213, 2444, 2962, 3247, 3935, 4292, 5149, 5579, 6674, 7247, 8590, 9221, 10964, 11804, 13870, 14843, 17480, 18675, 21866 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A knapsack partition (A108917, A299702) is an integer partition such that every submultiset has a different sum. The one non-knapsack partition counted under a(4) is (2,1,1).

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 three non-knapsack partitions counted under a(6) are:

  (2,2,1,1)

  (3,1,1,1)

  (2,1,1,1,1)

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], UnsameQ@@Plus@@@Subsets[Union[#]]&]], {n, 0, 20}]

CROSSREFS

Dominates A108917.

Cf. A002033, A034444, A196723, A275972, A276024, A299702, A325592, A325856, A325863, A325864, A325865, A325877.

Sequence in context: A116480 A023026 A096778 * A280277 A102108 A105780

Adjacent sequences:  A325859 A325860 A325861 * A325863 A325864 A325865

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 31 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 March 31 19:37 EDT 2020. Contains 333151 sequences. (Running on oeis4.)