%I #5 Mar 11 2023 18:26:27
%S 0,1,5,31,248,2382,27233,359800,5364193,88622485,1602171855,
%T 31410476113,663240471075,15001046054183,361775504849332,
%U 9266474332849318,251217335356943672,7186461542458525108,216332059500870350414,6835872042063656823802
%N Number of connected cubic graphs on 2n unlabeled vertices rooted at a pair of indistinguishable vertices.
%F G.f.: B(x)/C(x) - (D(x) + D(x^2))/2 where B(x), C(x) and D(x) are the g.f.s of A361411, A005638 and A361407, respectively.
%Y Column k=2 of A321304.
%Y Cf. A002851, A005638, A361407, A361411.
%K nonn
%O 1,3
%A _Andrew Howroyd_, Mar 11 2023