A051390 Number of nonisomorphic Steiner quadruple systems (SQS's) of order n.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• hard

Examples

			There are 4 nonisomorphic SQS's on 14 points.
		

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. Jeffrey H. Dinitz and D. R. Stinson, Wiley, 1992.

Links

• Petteri Kaski, Patric 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

Crossrefs

See A124120, A124119 for other versions of this sequence. The present entry is the official version.

Cf. A030129, A001201, A030128.

Formula

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