A129429 Number of isomorphism classes of 4-regular multigraphs of order n, loops allowed.

1, 3, 7, 20, 56, 187, 654, 2705, 12587, 67902, 417065, 2897432, 22382255, 189930004, 1750561160, 17380043136, 184653542135, 2088649831822, 25046462480066, 317295911519901, 4233450347175663, 59329632953577985, 871281036897298464

Offset: 1

Author

Brendan McKay, Apr 15 2007

Keywords

• nonn

Comments

Initial terms computed using software at http://users.cecs.anu.edu.au/~bdm/nauty/

Equation (5.8) of Read's paper tells us a(n) = N {S_n[S_4] * S_{2n}[S_2]}, where we are working with cycle index polynomials. - Jason Kimberley, Oct 05 2009

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..40
• R. de Mello Koch and S. Ramgoolam, Strings from Feynman graph counting: Without large N, Phys. Rev. D 85 (2012) 026007
• R. C. Read, The enumeration of locally restricted graphs (I), J. London Math. Soc. 34 (1959) 417-436.

Crossrefs

Column k=4 of A167625.

Cf. A085549 (connected), A129418, A129427, A129431, A129433, A129435, A129437.

Formula

Euler transform of A085549. - Andrew Howroyd, Mar 15 2020

Extensions

Using equation (5.8) of Read's paper, new terms a(17)-a(19) were computed in MAGMA by Jason Kimberley, Oct 05 2009

Four more terms a(20)-a(23) also computed by Jason Kimberley, Nov 09 2009