A129427 Number of isomorphism classes of 3-regular multigraphs of order 2n, loops allowed.

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

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.

R. de Mello Koch, S. Ramgoolam, Strings from Feynman graph counting: Without large N, Phys. Rev. D 85 (2012) 026007

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) 417-436. - 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(QQ).homogeneous()
def A129427(n):
    X = h([2*n]).plethysm(h([3]))
    Y = h([3*n]).plethysm(h([2]))
    return X.scalar(Y)
# Bruce Westbury, Aug 16 2013

Crossrefs

Column k=3 of A167625.

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(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