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A050535 Number of multigraphs on infinite set of nodes with n edges. 26
1, 1, 3, 8, 23, 66, 212, 686, 2389, 8682, 33160, 132277, 550835, 2384411, 10709827, 49782637, 238998910, 1182772364, 6023860266, 31525780044, 169316000494, 932078457785, 5253664040426, 30290320077851, 178480713438362, 1073918172017297 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also, a(n) is the number of n-rowed binary matrices with all row sums equal to 2, up to row and column permutation (see Jovovic's formula). Also, a(n) is the limit of A192517(m,n) as m grows. - Max Alekseyev, Oct 18 2017

Row sums of the triangle defined by the Multiset Transformation of A076864,

1 ;

0 1;

0 2 1;

0 5 2 1;

0 12 8 2 1;

0 33 22 8 2 1;

0 103 72 26 8 2 1;

0 333 229 87 26 8 2 1;

0 1183 782 295 92 26 8 2 1;

0 4442 2760 1036 315 92 26 8 2 1;

0 17576 10270 3735 1129 321 92 26 8 2 1;

0 72810 39770 13976 4117 1154 321 92 26 8 2 1;

0 314595 160713 54132 15547 4237 1161 321 92 26 8 2 1;

- R. J. Mathar, Jul 18 2017

Also the number of non-isomorphic set multipartitions (multisets of sets) of {1, 1, 2, 2, 3, 3, ..., n, n}. - Gus Wiseman, Jul 18 2018

REFERENCES

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 88, Eq. (4.1.18).

LINKS

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

F. Harary, The number of linear, directed, rooted, and connected graphs, Trans. Am. Math. Soc. 78 (1955) 445-463, eq. (24).

V. Jovovic, Number of m-rowed binary matrices with all row sums equal to n, up to row and column permutation

Patrick T. Komiske, Eric M. Metodiev, Jesse Thaler, Energy flow polynomials: A complete linear basis for jet substructure, arXiv:1712.07124 [hep-ph], 2017.

FORMULA

a(n) = A192517(2*n,n) = A192517(m,n) for any m>=2*n. - Max Alekseyev, Oct 18 2017

EXAMPLE

From Gus Wiseman, Jul 18 2018: (Start)

Non-isomorphic representatives of the a(3) = 8 set multipartitions of {1, 1, 2, 2, 3, 3}:

  (123)(123)

  (1)(23)(123)

  (12)(13)(23)

  (1)(1)(23)(23)

  (1)(2)(3)(123)

  (1)(2)(13)(23)

  (1)(1)(2)(3)(23)

  (1)(1)(2)(2)(3)(3)

(End)

CROSSREFS

Cf. A001399, A003082, A014395, A014396, A014397, A014398.

Cf. A058389, A050913, A058783, A058390, A058784, A058785, A058391, A058392, A001501, A058528.

Cf. A007716, A007717, A020555, A050535, A094574, A316974.

Sequence in context: A116410 A199841 A106606 * A025578 A038151 A230122

Adjacent sequences:  A050532 A050533 A050534 * A050536 A050537 A050538

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Dec 29 1999

EXTENSIONS

More terms from Sean A. Irvine, Oct 02 2011

STATUS

approved

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Last modified September 19 04:25 EDT 2018. Contains 315155 sequences. (Running on oeis4.)