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%I #29 Mar 07 2023 15:04:59
%S 1,3,7,20,56,187,654,2705,12587,67902,417065,2897432,22382255,
%T 189930004,1750561160,17380043136,184653542135,2088649831822,
%U 25046462480066,317295911519901,4233450347175663,59329632953577985,871281036897298464
%N Number of isomorphism classes of 4-regular multigraphs of order n, loops allowed.
%C Initial terms computed using software at http://users.cecs.anu.edu.au/~bdm/nauty/
%C 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
%H Andrew Howroyd, <a href="/A129429/b129429.txt">Table of n, a(n) for n = 1..40</a>
%H R. de Mello Koch and S. Ramgoolam, <a href="https://doi.org/10.1103/PhysRevD.85.026007">Strings from Feynman graph counting: Without large N</a>, Phys. Rev. D 85 (2012) 026007
%H R. C. Read, <a href="http://dx.doi.org/10.1112/jlms/s1-34.4.417">The enumeration of locally restricted graphs (I)</a>, J. London Math. Soc. 34 (1959) 417-436.
%F Euler transform of A085549. - _Andrew Howroyd_, Mar 15 2020
%Y Column k=4 of A167625.
%Y Cf. A085549 (connected), A129418, A129427, A129431, A129433, A129435, A129437.
%K nonn
%O 1,2
%A _Brendan McKay_, Apr 15 2007
%E Using equation (5.8) of Read's paper, new terms a(17)-a(19) were computed in MAGMA by _Jason Kimberley_, Oct 05 2009
%E Four more terms a(20)-a(23) also computed by _Jason Kimberley_, Nov 09 2009
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