[go: up one dir, main page]

login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A371796 Number of quanimous subsets of {1..n}, meaning there is more than one set partition with all equal block-sums. 23
0, 0, 0, 1, 3, 8, 19, 43, 94, 206, 439 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
A finite multiset of numbers is defined to be quanimous iff it can be partitioned into two or more multisets with equal sums. Quanimous partitions are counted by A321452 and ranked by A321454.
LINKS
EXAMPLE
The set s = {3,4,6,8,9} has set partitions {{3,4,6,8,9}} and {{3,4,8},{6,9}} with equal block-sums, so s is counted under a(9).
The a(3) = 1 through a(6) = 19 subsets:
{1,2,3} {1,2,3} {1,2,3} {1,2,3}
{1,3,4} {1,3,4} {1,3,4}
{1,2,3,4} {1,4,5} {1,4,5}
{2,3,5} {1,5,6}
{1,2,3,4} {2,3,5}
{1,2,4,5} {2,4,6}
{2,3,4,5} {1,2,3,4}
{1,2,3,4,5} {1,2,3,6}
{1,2,4,5}
{1,2,5,6}
{1,3,4,6}
{2,3,4,5}
{2,3,5,6}
{3,4,5,6}
{1,2,3,4,5}
{1,2,3,4,6}
{1,2,4,5,6}
{2,3,4,5,6}
{1,2,3,4,5,6}
MATHEMATICA
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]& /@ sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
Table[Length[Select[Subsets[Range[n]], Length[Select[sps[#], SameQ@@Total/@#&]]>1&]], {n, 0, 10}]
CROSSREFS
The "bi-" version for integer partitions is A002219 aerated, ranks A357976.
The "bi-" version for strict partitions is A237258 aerated, ranks A357854.
The complement for integer partitions is A321451, ranks A321453.
The version for integer partitions is A321452, ranks A321454
The version for strict partitions is A371737, complement A371736.
The complement is counted by A371789, differences A371790.
The "bi-" version is A371791, complement A371792.
First differences are A371797.
A108917 counts knapsack partitions, ranks A299702, strict A275972.
A366754 counts non-knapsack partitions, ranks A299729, strict A316402.
A371783 counts k-quanimous partitions.
Sequence in context: A008466 A102712 A054480 * A191787 A347310 A332719
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Apr 17 2024
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 29 13:55 EDT 2024. Contains 375517 sequences. (Running on oeis4.)