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%I #19 Feb 02 2020 21:40:47
%S 1,1,0,1,0,0,0,1,0,1,0,0,0,4,0,1054163
%N Number of nonisomorphic Steiner quadruple systems (SQS's) of order n.
%D CRC Handbook of Combinatorial Designs, 1996, circa p. 70.
%D 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.
%H Petteri Kaski, Patric R. J. Östergård (Patric.Ostergard(AT)hut.fi) and O. Pottonen, <a href="http://dx.doi.org/10.1016/j.jcta.2006.03.017">The Steiner quadruple systems of order 16</a>, Journal of Combinatorial Theory, Series A, Volume 113, Issue 8, November 2006, Pages 1764-1770.
%H V. A. Zinoviev and D. V. Zinoviev, <a href="http://www.mathe2.uni-bayreuth.de/axel/papers/zinoviev:classification_of_steiner_quadruple_systems_of_order_16_and_rank_14.pdf">Classification of Steiner Quadruple Systems of order 16 and rank 14</a>, [English translation from Russian], Problemy Peredachi Informatsii, 42 (No. 3, 2006), 59-72.
%H V. A. Zinoviev and D. V. Zinoviev, <a href="http://dx.doi.org/10.1134/S0032946006030057">Classification of Steiner Quadruple Systems of order 16 and rank 14</a>, 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.
%H <a href="/index/St#Steiner">Index entries for sequences related to Steiner systems</a>
%F a(n) = 0 unless n = 1 or n == 2 or 4 (mod 6).
%e There are 4 nonisomorphic SQS's on 14 points.
%Y See A124120, A124119 for other versions of this sequence. The present entry is the official version.
%Y Cf. A030129, A001201, A030128.
%K nonn,nice,hard
%O 1,14
%A _N. J. A. Sloane_
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