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!)
A320395 Number of non-isomorphic 3-uniform multiset systems over {1,...,n}. 8
1, 2, 10, 208, 45960, 287800704, 100103176111616, 3837878984050795692032, 32966965900633495618246298767360, 128880214965936601447070466061615999984402432, 464339910355487357558396669850788946402420533504952464572416 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..25

EXAMPLE

Non-isomorphic representatives of the a(2) = 10 multiset systems:

  {}

  {{111}}

  {{122}}

  {{111}{222}}

  {{112}{122}}

  {{112}{222}}

  {{122}{222}}

  {{111}{122}{222}}

  {{112}{122}{222}}

  {{111}{112}{122}{222}}

MATHEMATICA

Table[Sum[2^PermutationCycles[Ordering[Map[Sort, Select[Tuples[Range[n], 3], OrderedQ]/.Rule@@@Table[{i, prm[[i]]}, {i, n}], {1}]], Length], {prm, Permutations[Range[n]]}]/n!, {n, 6}]

PROG

(PARI)

permcount(v)={my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}

rep(typ)={my(L=List(), k=0); for(i=1, #typ, k+=typ[i]; listput(L, k); while(#L<k, listput(L, #L))); Vec(L)}

can(v, f)={my(d=1, u=v); while(d>0, u=vecsort(apply(f, u)); d=lex(u, v)); !d}

Q(perm)={my(t=0); forsubset([#perm+2, 3], v, t += can([v[1], v[2]-1, v[3]-2], t->perm[t])); t}

a(n)={my(s=0); forpart(p=n, s += permcount(p)*2^Q(rep(p))); s/n!} \\ Andrew Howroyd, Aug 26 2019

CROSSREFS

The 2-uniform case is A000666. The case of sets (as opposed to multisets) is A000665. The case of labeled spanning sets is A302374, with unlabeled case A322451.

Cf. A000088, A000612, A003180, A070166, A301922, A317795, A319876.

Sequence in context: A246532 A159558 A297066 * A001528 A293148 A193482

Adjacent sequences:  A320392 A320393 A320394 * A320396 A320397 A320398

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 12 2018

EXTENSIONS

Terms a(9) and beyond from Andrew Howroyd, Aug 26 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 February 17 02:22 EST 2020. Contains 331976 sequences. (Running on oeis4.)