A318590 -id:A318590 - cp's OEIS frontend

A053465 Number of connected 2-multigraphs on n nodes.

1, 1, 2, 7, 53, 712, 24576, 2275616, 589543159, 420188096140, 819411181635025, 4381819315336997184, 64583749250393921183423, 2638507778912832094660037006, 300397569392490080058575760090548, 95776592061550107555640978862165082446

Offset: 0

Vladeta Jovovic, Jan 13 2000

A 2-multigraph is similar to an ordinary graph except there are 0, 1 or 2 edges between any two nodes (self-loops are not allowed).

Also the number of connected signed graphs on n unlabeled nodes. - Andrew Howroyd, Sep 25 2018

Andrew Howroyd, Table of n, a(n) for n = 0..50
Edward A. Bender and E. Rodney Canfield, Enumeration of connected invariant graphs, Journal of Combinatorial Theory, Series B 34.3 (1983): 268-278. See p. 273.

Cf. A004102, A318590.

A004102 = Import["https://oeis.org/A004102/b004102.txt", "Table"][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
Join[{1}, EulerInvTransform[A004102 // Rest]] (* Jean-François Alcover, Sep 12 2019, after Andrew Howroyd, updated Mar 17 2020 *)

Inverse Euler transform of A004102. - Andrew Howroyd, Sep 25 2018

a(0)=1 prepended and terms a(15) and beyond from Andrew Howroyd, Sep 25 2018

A034892 Number of balanced signed graphs on n unlabeled nodes.

Original entry on oeis.org

1, 1, 3, 8, 39, 226, 2283, 36789, 1062679, 55717077, 5405078682, 972656526492, 325183692812200, 202373967993972497, 235081289816026793049, 511296223391186047847309, 2088912833728676472658628201, 16081914207958884651686215477871, 234010862353438997655954463710225233

Offset: 0

Ronald C. Read

R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.

Andrew Howroyd, Table of n, a(n) for n = 0..50
Wikipedia, Signed graph

Cf. A004102, A005142, A318590.

Euler transform of A318590.

Name clarified and offset corrected by Andrew Howroyd, Sep 25 2018

a(0)=1 prepended and terms a(13) and beyond from Andrew Howroyd, Sep 25 2018

cp's OEIS Frontend

A053465 Number of connected 2-multigraphs on n nodes.

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