%I
%S 1,1,0,1,0,0,0,30,0,2520,0,0,0,37362124800,0,14311959985625702400,0,0,
%T 0
%N Number of Steiner quadruple systems (SQS's) of order n.
%C 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.
%C 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
%C 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.
%D Petteri Kaski, Patric R. J. Östergård (Patric.Ostergard(AT)hut.fi) and O. Pottonen, The Steiner quadruple systems of order 16
%D 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
%H Vesa Linjaaho, <a href="http://www.ct.tkk.fi/~vesa/">Home Page</a>.
%H Vesa Linjaaho, <a href="/A137348/a137348.txt">Python program</a>
%H <a href="/index/St#Steiner">Index entries for sequences related to Steiner systems</a>
%e There are 2520 SQS's on 10 points.
%K hard,nonn
%O 1,8
%A Vesa Linjaaho (vesa.linjaaho(AT)tkk.fi), Apr 08 2008, May 13 2008
