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A003049 Number of connected Eulerian graphs with n unlabeled nodes.
(Formerly M3344)
1, 0, 1, 1, 4, 8, 37, 184, 1782, 31026, 1148626, 86539128, 12798435868, 3620169692289, 1940367005824561, 1965937435288738165, 3766548132138130650270, 13666503289976224080346733 (list; graph; refs; listen; history; text; internal format)



These are connected graphs with every node of even degree (cf. A002854).


F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 117.

Valery A. Liskovets, Enumeration of Euler graphs. (Russian), Vesci Akad. Navuk BSSR, Ser. Fiz.-Mat. Navuk 1970, No.6, 38-46 (1970). Math. Rev., Vol. 44, 1972, p. 1195, #6557.

R. W. Robinson, Enumeration of Euler graphs, pp. 147-153 of F. Harary, editor, Proof Techniques in Graph Theory. Academic Press, NY, 1969.

R. W. Robinson, personal communication.

R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1979.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


R. W. Robinson, Table of n, a(n) for n = 1..26

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

Erich Friedman, Illustration of initial terms

V. A. Liskovec, Enumeration of Euler Graphs, (in Russian), Akademiia Navuk BSSR, Minsk., 6 (1970), 38-46. (annotated scanned copy)

C. L. Mallows and N. J. A. Sloane, Two-graphs, switching classes and Euler graphs are equal in number, SIAM J. Appl. Math., 28 (1975), 876-880.

C. L. Mallows and N. J. A. Sloane, Two-graphs, switching classes and Euler graphs are equal in number, SIAM J. Appl. Math., 28 (1975), 876-880. [Copy on N. J. A. Sloane's Home Page]

Brendan McKay, Combinatorial Data (Eulerian graphs)

Peter Steinbach, Field Guide to Simple Graphs, Volume 1, Part 17 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)

Eric Weisstein's World of Mathematics, Eulerian Graph.


Let B(x) = g.f. for A002854. Then g.f. A(x) for A003049 satisfies 1+B(x) = exp( Sum_{n=1..inf} A(x^n)/n). - Robinson (1969).

Inverse Euler transform of A002854. (This is equivalent to the Robinson formula.) - Franklin T. Adams-Watters, Jul 24 2006


Cf. A002854.

Sequence in context: A229535 A047710 A063580 * A098563 A231398 A231465

Adjacent sequences:  A003046 A003047 A003048 * A003050 A003051 A003052




N. J. A. Sloane.


More terms from Vladeta Jovovic, Apr 18 2000



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Last modified June 27 09:37 EDT 2017. Contains 288788 sequences.