A165434 Number of tri-coverings of a set.
1, 1, 4, 39, 862, 35775, 2406208, 238773109, 32867762616, 6009498859909, 1412846181645855, 416415343791239162, 150747204270574506888, 65905473934553360340713, 34305461329980340135062217, 21003556204331356488142290707, 14967168378184553824642693791437
Offset: 0
Keywords
Examples
For n=2, a(2)=4, since if you have two sets of identical triples the A-brothers and the B-sisters, and you want to arrange them into a multiset of nonempty sets, where no one is allowed to cohabitate with his or her sibling, the following are possible 1.{{AB},{AB},{AB}} 2.{{AB},{AB},{A},{B}} 3.{{AB},{A},{A},{B},{B}} 4.{{A},{A},{A},{B},{B},{B}}.
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..100
- E. A. Bender, Partitions of multisets, Discrete Mathematics 9 (1974) 301-312.
- J. S. Devitt and D. M. Jackson, The enumeration of covers of a finite set, J. London Math. Soc.(2) 25 (1982), 1-6.
- Doron Zeilberger, In How Many Ways Can You Reassemble Several Russian Dolls?, has links to more terms and related sequences
- Doron Zeilberger, In How Many Ways Can You Reassemble Several Russian Dolls?, arXiv:0909.3453 [math.CO], 2009.
- Doron Zeilberger, BABUSHKAS; Local copy
Programs
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Maple
Do SeqBrn(3,n); in the Maple package BABUSHKAS (see links) where n+1 is the number of desired terms.
Extensions
Edited by Charles R Greathouse IV, Oct 28 2009