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%I #13 Mar 04 2020 05:54:11
%S 0,0,0,0,0,0,1,1,3,10,25,95,366,1433,5802,24105,102479,445577,1992044
%N Number of self-dual combinatorial configurations of type (n_3).
%C A combinatorial configuration of type (n_3) consists of an (abstract) set of n points together with a set of n triples of points, called lines, such that each point belongs to 3 lines and each line contains 3 points.
%C Interchanging the roles of points and lines gives the dual configuration. A configuration is self-dual if there is an isomorphism from it to its dual.
%H A. Betten, G. Brinkmann and T. Pisanski, <a href="https://doi.org/10.1016/S0166-218X(99)00143-2">Counting symmetric configurations v_3</a>, Discrete Appl. Math., 99 (2000), 331-338.
%H T. Pisanski, M. Boben, D. MaruĊĦic, A. Orbanic, A. Graovac, <a href="https://doi.org/10.1016/S0012-365X(03)00110-9">The 10-cages and derived configurations</a>, Discrete Math. 275 (2004), 265-276.
%e Example: the Fano plane is the only (7_3) configuration and is self-dual. It contains 7 points 1,2,...7 and 7 triples, 124, 235, 346, 457, 561, 672, 713.
%e The unique (8_3) configuration is also self-dual. It consists of the triples 125, 148, 167, 236, 278, 347, 358, 456.
%Y Cf. A001403 (configurations (n_3), with many further references), A099999, A023994.
%Y See also A005787, A000698, A098702, A098804, A098822, A098841, A098851, A098852, A098854
%K nonn,nice,hard,more
%O 1,9
%A _N. J. A. Sloane_, Nov 05 2004
%E a(1)-a(18) from the Betten, Brinkmann and Pisanski article.
%E a(19) from the Pisanski et al. article.
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