

A051390


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


7



1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 4, 0, 1054163
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OFFSET

1,14


REFERENCES

CRC Handbook of Combinatorial Designs, 1996, circa p. 70.
A. Hartman and K. T. Phelps, Steiner quadruple systems, pp. 205240 of Contemporary Design Theory, ed. J. H. Dinitz and D. R. Stinson, Wiley, 1992.


LINKS

Table of n, a(n) for n=1..16.
P. Kaski, P. R. J. Östergård (Patric.Ostergard(AT)hut.fi) and O. Pottonen, The Steiner quadruple systems of order 16, Journal of Combinatorial Theory, Series A, Volume 113, Issue 8, November 2006, Pages 17641770.
V. A. Zinoviev and D. V. Zinoviev, Classification of Steiner Quadruple Systems of order 16 and rank 14, [English translation from Russian], Problemy Peredachi Informatsii, 42 (No. 3, 2006), 5972.
V. A. Zinoviev and D. V. Zinoviev, Classification of Steiner Quadruple Systems of order 16 and rank 14, Problems of Information Transmission, JulySeptember 2006, Volume 42, Issue 3, pp 217229; from [in Russian], Problemy Peredachi Informatsii, 42 (No. 3, 2006), 5972.
Index entries for sequences related to Steiner systems


FORMULA

a(n) = 0 unless n = 1 or n == 2 or 4 mod 6.


EXAMPLE

There are 4 nonisomorphic SQS's on 14 points.


CROSSREFS

See A124120, A124119 for other versions of this sequence. The present entry is the official version.
Cf. A030129, A001201, A030128.
Sequence in context: A130105 A013463 A013464 * A124120 A320742 A093318
Adjacent sequences: A051387 A051388 A051389 * A051391 A051392 A051393


KEYWORD

nonn,nice,hard


AUTHOR

N. J. A. Sloane


STATUS

approved



