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A240117 Schoenheim lower bound L(n,6,2).

%I A240117 #14 Jan 26 2019 14:27:31
%S A240117 1,3,3,3,4,4,6,7,7,8,8,12,12,13,14,14,19,20,20,21,22,27,28,29,30,31,
%T A240117 38,39,40,41,42,50,51,52,54,55,63,65,66,68,69,79,80,82,84,85,96,98,99,
%U A240117 101,103,114,116,118,120,122,135,137,139,141,143,157,159,161
%N A240117 Schoenheim lower bound L(n,6,2).
%H A240117 Colin Barker, <a href="/A240117/b240117.txt">Table of n, a(n) for n = 6..1000</a>
%H A240117 D. Gordon, G. Kuperberg and O. Patashnik, <a href="http://arxiv.org/abs/math/9502238">New constructions for covering designs</a>, arXiv:math/9502238 [math.CO], 1995.
%F A240117 Empirical g.f.: x^6*(x^35 -x^31 -x^30 +2*x^26 +x^23 +x^20 -x^18 +x^17 +x^16 +x^13 -x^12 +2*x^11 +x^7 -x^5 +x^4 +2*x +1) / ( -x^36 +x^35 +x^31 -x^30 +x^6 -x^5 -x +1).
%t A240117 schoenheim[n_, k_, t_] := Module[{lb = 1, n1 = n, k1 = k, t1 = t}, n1 += 1 - t1; k1 += 1 - t1; While[t1 > 0, lb = Ceiling[(lb*n1)/k1]; t1--; n1++; k1++]; lb];
%t A240117 Table[schoenheim[n, 6, 2], {n, 6, 100}] (* _Jean-François Alcover_, Jan 26 2019, from PARI *)
%o A240117 (PARI) schoenheim(n, k, t) = {
%o A240117   my(lb = 1);
%o A240117   n += 1-t; k += 1-t;
%o A240117   while(t>0,
%o A240117     lb = ceil((lb*n)/k);
%o A240117     t--; n++; k++
%o A240117   );
%o A240117   lb
%o A240117 }
%o A240117 s=[]; for(n=6, 100, s=concat(s, schoenheim(n, 6, 2))); s
%Y A240117 Cf. A240115, A240116, A240118, A240119.
%Y A240117 Cf. A011975, A036831, A036832, A036833, A036834, A036835, A036836.
%K A240117 nonn
%O A240117 6,2
%A A240117 _Colin Barker_, Apr 01 2014