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Number of isomorphism classes of 5-regular multigraphs of order 2n, loops allowed.
8

%I #21 Mar 22 2020 02:41:18

%S 3,32,727,42703,5988679,1639714425,757559332934,541249158493444,

%T 564262722366313620,822164422526588575949,1618567795242262158194706,

%U 4188563149202582371775198174,13926836449718334345103644635724,58360974360850795591633858610837541

%N Number of isomorphism classes of 5-regular multigraphs of order 2n, loops allowed.

%C First seven terms were computed using software at http://users.cecs.anu.edu.au/~bdm/nauty/

%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. [From _Jason Kimberley_, Oct 05 2009]

%F a(n) = N\{S_{2n}[S_5] * S_{5n}[S_2]\}. - _Jason Kimberley_, Oct 05 2009

%F Euler transform of A129430. - _Andrew Howroyd_, Mar 15 2020

%Y Column k=5 of A167625.

%Y Cf. A129430, A129420, A129427, A129429, A129433, A129435, A129437.

%K nonn

%O 1,1

%A _Brendan McKay_, Apr 15 2007

%E Using equation (5.8) of Read 1959, new terms a(8)-a(10) were computed in MAGMA during 2009 by _Jason Kimberley_, Dec 22 2010

%E a(11)-a(14) from _Andrew Howroyd_, Mar 21 2020