

A100001


Number of selfdual combinatorial configurations of type (n_3).


3



0, 0, 0, 0, 0, 0, 1, 1, 3, 10, 25, 95, 366, 1433, 5802, 24105, 102479, 445577, 1992044
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OFFSET

1,9


COMMENTS

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.
Interchanging the roles of points and lines gives the dual configuration. A configuration is selfdual if there is an isomorphism from it to its dual.


REFERENCES

A. Betten, G. Brinkmann and T. Pisanski, Counting symmetric configurations v_3, Discrete Appl. Math., 99 (2000), 331338.
Pisanski, T.; Boben, M.; Marusic, D.; Orbanic, A.; and Graovac, A. The 10cages and derived configurations. Discrete Math. 275 (2004), 265276.


LINKS

Table of n, a(n) for n=1..19.


EXAMPLE

Example: the Fano plane is the only (7_3) configuration and is selfdual. It contains 7 points 1,2,...7 and 7 triples, 124, 235, 346, 457, 561, 672, 713.
The unique (8_3) configuration is also selfdual. It consists of the triples 125, 148, 167, 236, 278, 347, 358, 456.


CROSSREFS

Cf. A001403 (configurations (n_3), with many further references), A099999, A023994.
See also A005787, A000698, A098702, A098804, A098822, A098841, A098851, A098852, A098854
Sequence in context: A131433 A110713 A098702 * A227937 A190529 A212967
Adjacent sequences: A099998 A099999 A100000 * A100002 A100003 A100004


KEYWORD

nonn,nice,hard


AUTHOR

N. J. A. Sloane, Nov 05 2004


EXTENSIONS

a(1)a(18) from the Betten, Brinkmann and Pisanski article.
a(19) from the Pisanski et al. article.


STATUS

approved



