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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,14

REFERENCES

CRC Handbook of Combinatorial Designs, 1996, circa p. 70.

A. Hartman and K. T. Phelps, Steiner quadruple systems, pp. 205-240 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 1764-1770.

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), 59-72.

V. A. Zinoviev and D. V. Zinoviev, Classification of Steiner Quadruple Systems of order 16 and rank 14, Problems of Information Transmission, July-September 2006, Volume 42, Issue 3, pp 217-229; from [in Russian], Problemy Peredachi Informatsii, 42 (No. 3, 2006), 59-72.

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: A013464 A306819 A327113 * A124120 A320742 A093318

Adjacent sequences:  A051387 A051388 A051389 * A051391 A051392 A051393

KEYWORD

nonn,nice,hard

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 16 21:10 EDT 2019. Contains 328103 sequences. (Running on oeis4.)