

A137348


Number of Steiner quadruple systems (SQS's) of order n.


1



1, 1, 0, 1, 0, 0, 0, 30, 0, 2520, 0, 0, 0, 37362124800, 0, 14311959985625702400, 0, 0, 0
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OFFSET

1,8


COMMENTS

The values are calculated by utilizing the Knuth's Algorithm X. Only the number of nonisomorphic SQS's is presented in peerreviewed literature and scientific textbooks. The algorithm was verified to be valid by seeking STS's presented in A001201.
n=14 calculated from "Mendelsohn and Hung: On Steiner Systems S(3,4,14) and S(4,5,15), Util. Math. Vol 1 (1972), pp. 595" with orbitstabilizer theorem
n=15 is given in "Petteri Kaski, Patric R. J. Östergård (Patric.Ostergard(AT)hut.fi) and O. Pottonen, The Steiner quadruple systems of order 16". SQS(20) is still unknown.


REFERENCES

Petteri Kaski, Patric R. J. Östergård (Patric.Ostergard(AT)hut.fi) and O. Pottonen, The Steiner quadruple systems of order 16
N. S. Mendelsohn and S. H. Y. Hung, On the Steiner Systems S(3,4,14) and S(4,5,15), Util. Math. Vol. 1, 1972, pp. 595


LINKS

Table of n, a(n) for n=1..19.
Vesa Linjaaho, Home Page.
Vesa Linjaaho, Python program
Index entries for sequences related to Steiner systems


EXAMPLE

There are 2520 SQS's on 10 points.


CROSSREFS

Sequence in context: A277043 A198805 A030128 * A137737 A262706 A062513
Adjacent sequences: A137345 A137346 A137347 * A137349 A137350 A137351


KEYWORD

hard,nonn


AUTHOR

Vesa Linjaaho (vesa.linjaaho(AT)tkk.fi), Apr 08 2008, May 13 2008


STATUS

approved



