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%I #5 Nov 10 2007 03:00:00
%S 0,0,0,1,1,5,19,153,1615,25180,479238,10695820
%N Number of nonisomorphic configurations of degree >= 2 (or generators) of n triples in Steiner triple systems.
%C A configuration is a set of triples (of points) where every pair of points occurs in at most one triple. (A Steiner triple system is a set of triples where every pair occurs exactly once; thus configurations are often called partial Steiner triple systems). The triples are also called blocks.
%C A 'generator' is 'a configuration where every point occurs in at least two blocks'. The term refers to the work of Horak, Phillips, Wallis & Yucas, who show that the number of occurrences of a configuration in a Steiner triple system is expressible as a linear form in the numbers of occurrences of the generators.
%C If you relax the restriction on the number of times a pair of points can occur in a configuration - so that a configuration is just any multi-set of triples - then we get A050913.
%D Forbes, Grannell & Griggs, 'Configurations and trades in Steiner triple systems', in preparation.
%D Mike Grannell and Terry Griggs, 'Configurations in Steiner triple systems', in Combinatorial Designs and their Applications, Chapman & Hall, CRC Research Notes in Math. 403 (1999), 103-126.
%D Horak, P., Phillips, N. K. C., Wallis, W. D. and Yucas, J. L., Counting frequencies of configurations in Steiner triple systems. Ars Combin. 46 (1997), 65-75.
%Y Cf. A082789, A050913.
%K nonn
%O 1,6
%A T. Forbes (anthony.d.forbes(AT)googlemail.com), May 24 2003
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