

A129427


Number of isomorphism classes of 3regular multigraphs of order 2n, loops allowed.


9



1, 2, 8, 31, 140, 722, 4439, 32654, 289519, 3054067, 37584620, 527968286, 8308434931, 144345554051, 2738280739075, 56245013793246, 1242596591479816, 29366532494796900, 739033832149588904, 19726887762569763453
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OFFSET

0,2


COMMENTS

a(1)..a(11) computed using software at http://users.cecs.anu.edu.au/~bdm/nauty/


REFERENCES

P. A. Morris, Letter to N. J. A. Sloane, Mar 02 1971.


LINKS

Table of n, a(n) for n=0..19.
P. A. Morris, Letter to N. J. A. Sloane, Mar 02 1971.
R. C. Read, The enumeration of locally restricted graphs (I), J. London Math. Soc. 34 (1959) 417436.  Jason Kimberley, Sep 17 2009


FORMULA

a(n)=N\{S_{2n}[S_3] * S_{3n}[S_2]\}.  Jason Kimberley, Sep 17 2009


PROG

(Sage)
h = SymmetricFunctions(ZZ).homogeneous()
h([2*n]).plethysm(h([3]).scalar(h([3*n]).plethysm(h([2])))
# Bruce Westbury, Aug 16 2013


CROSSREFS

Cf. A005967 (connected, inv. Euler trans.), A129416, A129429, A129431, A129433, A129435, A129437, A005638.
Sequence in context: A009567 A150819 A003175 * A150820 A150821 A150822
Adjacent sequences: A129424 A129425 A129426 * A129428 A129429 A129430


KEYWORD

nonn


AUTHOR

Brendan McKay, Apr 15 2007


EXTENSIONS

Using equation (5.8) of Read 1959, new terms a(12) and a(13) were computed in MAGMA by Jason Kimberley, Sep 17 2009
Further terms a(14),a(15),a(16) also computed by Jason Kimberley, announced Nov 09 2009
Formula corrected from n vertices to 2n vertices by Jason Kimberley, Nov 09 2009
Added a(0).  N. J. A. Sloane, Aug 26 2013
a(17)a(19) from Sean A. Irvine, Oct 29 2016


STATUS

approved



