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%I #39 Dec 21 2023 11:58:38
%S 0,0,0,0,0,0,1,3,26,340,7297,233608
%N Number of Harris graphs with n vertices. Harris graphs are 1-tough, Eulerian graphs that are non-Hamiltonian.
%C There are no Harris graphs with 6 or fewer vertices.
%H Francesca Gandini, Shubhra Mishra, and Douglas Shaw, <a href="https://arxiv.org/abs/2312.10936">Families of Harris Graphs</a>, arXiv:2312.10936 [math.CO], 2023.
%H Shubhra Mishra, <a href="/A366315/a366315.png">Illustration for a(7) = 1: the unique minimal Harris graph of order 7</a>
%H Shubhra Mishra, <a href="/A366315/a366315_1.png">Illustration for a(8) = 3: the three order 8 Harris graphs</a>
%H Douglas J. Shaw, <a href="https://www.jstor.org/stable/48661740">Harris Graphs--A Graph Theory Activity for Students and Their Instructors</a>, The College Mathematics Journal, 49 (2018), 5, 323-326.
%e a(7)=1 because the only Harris graph of 7 vertices (0..6) has edges {(0,1), (0,2), (0,3), (0,4), (1,2), (1,3), (1,5), (2,3), (2,6), (3,4), (3,5), (3,6)}. - _Sean A. Irvine_, Oct 18 2023
%Y Cf. A007031.
%K nonn,more,hard
%O 1,8
%A _Shubhra Mishra_, Oct 06 2023
%E a(11)-a(12) from _Sean A. Irvine_, Oct 18 2023