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!)
A055621 Number of covers of an unlabeled n-set. 60
1, 1, 4, 34, 1952, 18664632, 12813206150470528, 33758171486592987151274638874693632, 1435913805026242504952006868879460423801146743462225386100617731367239680 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 78 (2.3.39)

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..12

Eric Weisstein's World of Mathematics, Cover

FORMULA

a(n) = (A003180(n) - A003180(n-1))/2 = A000612(n) - A000612(n-1) for n>0.

Euler transform of A323819. - Gus Wiseman, Aug 14 2019

EXAMPLE

There are 4 nonisomorphic covers of {1,2}, namely {{1},{2}}, {{1,2}}, {{1},{1,2}} and {{1},{2},{1,2}}.

From Gus Wiseman, Aug 14 2019: (Start)

Non-isomorphic representatives of the a(3) = 34 covers:

  {123}  {1}{23}    {1}{2}{3}      {1}{2}{3}{23}

         {13}{23}   {1}{3}{23}     {1}{2}{13}{23}

         {3}{123}   {2}{13}{23}    {1}{2}{3}{123}

         {23}{123}  {2}{3}{123}    {2}{3}{13}{23}

                    {3}{13}{23}    {1}{3}{23}{123}

                    {12}{13}{23}   {2}{3}{23}{123}

                    {1}{23}{123}   {3}{12}{13}{23}

                    {3}{23}{123}   {2}{13}{23}{123}

                    {13}{23}{123}  {3}{13}{23}{123}

                                   {12}{13}{23}{123}

.

  {1}{2}{3}{13}{23}     {1}{2}{3}{12}{13}{23}    {1}{2}{3}{12}{13}{23}{123}

  {1}{2}{3}{23}{123}    {1}{2}{3}{13}{23}{123}

  {2}{3}{12}{13}{23}    {2}{3}{12}{13}{23}{123}

  {1}{2}{13}{23}{123}

  {2}{3}{13}{23}{123}

  {3}{12}{13}{23}{123}

(End)

MAPLE

b:= proc(n, i, l) `if`(n=0, 2^(w-> add(mul(2^igcd(t, l[h]),

      h=1..nops(l)), t=1..w)/w)(ilcm(l[])), `if`(i<1, 0,

      add(b(n-i*j, i-1, [l[], i$j])/j!/i^j, j=0..n/i)))

    end:

a:= n-> `if`(n=0, 2, b(n$2, [])-b(n-1$2, []))/2:

seq(a(n), n=0..8);  # Alois P. Heinz, Aug 14 2019

MATHEMATICA

b[n_, i_, l_] := b[n, i, l] = If[n==0, 2^Function[w, Sum[Product[2^GCD[t, l[[h]]], {h, 1, Length[l]}], {t, 1, w}]/w][If[l=={}, 1, LCM@@l]], If[i<1, 0, Sum[b[n-i*j, i-1, Join[l, Table[i, {j}]]]/j!/i^j, {j, 0, n/i}]]];

a[n_] := If[n==0, 2, b[n, n, {}] - b[n-1, n-1, {}]]/2;

a /@ Range[0, 8] (* Jean-Fran├žois Alcover, Jan 31 2020, after Alois P. Heinz *)

CROSSREFS

Unlabeled set-systems are A000612 (partial sums).

The version with empty edges allowed is A003181.

The labeled version is A003465.

The T_0 case is A319637.

The connected case is A323819.

The T_1 case is A326974.

Cf. A058891, A319559, A326946, A326973.

Sequence in context: A088077 A162079 A113231 * A000860 A222397 A193994

Adjacent sequences:  A055618 A055619 A055620 * A055622 A055623 A055624

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Jun 04 2000

EXTENSIONS

More terms from David Moews (dmoews(AT)xraysgi.ims.uconn.edu) Jul 04 2002

a(0) = 1 prepended by Gus Wiseman, Aug 14 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 22 15:26 EST 2020. Contains 332137 sequences. (Running on oeis4.)