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A013922 Number of labeled connected graphs with n nodes and 0 cutpoints (blocks or nonseparable graphs). 4
0, 1, 1, 10, 238, 11368, 1014888, 166537616, 50680432112, 29107809374336, 32093527159296128, 68846607723033232640, 290126947098532533378816, 2417684612523425600721132544, 40013522702538780900803893881856 (list; graph; refs; listen; history; text; internal format)



Or, number of labeled 2-connected graphs with n nodes.


Miklos Bona, Handbook of Enumerative Combinatorics, CRC Press, 2015, p.402.

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 9.

Thomas Lange, Biconnected reliability, Hochschule Mittweida (FH), Fakultät Mathematik/Naturwissenschaften/Informatik, Master's Thesis, 2015.

R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.

Andrés Santos, Density Expansion of the Equation of State, in A Concise Course on the Theory of Classical Liquids, Volume 923 of the series Lecture Notes in Physics, pp 33-96, 2016. DOI:10.1007/978-3-319-29668-5_3. See Reference 40.

S. Selkow, The enumeration of labeled graphs by number of cut-points, Discr. Math. 185 (1998), 183-191.

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.20(b), g(n).


R. W. Robinson, Table of n, a(n) for n = 1..25

Huantian Cao, AutoGF: An Automated System to Calculate Coefficients of Generating Functions.


Harary and Palmer give e.g.f. in Eqn. (1.3.3) on page 10.


Cf. A002218, A004115. Row sums of triangle A123534.

Sequence in context: A096331 A159497 A177595 * A215835 A006423 A067423

Adjacent sequences:  A013919 A013920 A013921 * A013923 A013924 A013925




Stanley Selkow (sms(AT)owl.WPI.EDU)



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Last modified March 23 18:56 EDT 2018. Contains 301127 sequences. (Running on oeis4.)