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A240115 Schoenheim lower bound L(n,4,2).

%I A240115 #21 Jan 10 2024 20:17:54
%S A240115 1,3,3,4,6,7,8,11,12,13,18,19,20,26,27,29,35,37,39,46,48,50,59,61,63,
%T A240115 73,75,78,88,91,94,105,108,111,124,127,130,144,147,151,165,169,173,
%U A240115 188,192,196,213,217,221,239,243,248,266,271,276,295,300,305,326
%N A240115 Schoenheim lower bound L(n,4,2).
%C A240115 Only differs from A011976 when n = 7, 9, 10, or 19. - _Nathaniel Johnston_, Jan 10 2024
%H A240115 Colin Barker, <a href="/A240115/b240115.txt">Table of n, a(n) for n = 4..1000</a>
%H A240115 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 A240115 Empirical g.f.: x^4*(x^15 -x^13 -x^12 +2*x^10 +x^7 +x^5 +2*x +1) / ( -x^16 +x^15 +x^13 -x^12 +x^4 -x^3 -x +1).
%F A240115 a(n) = ceiling((n/4)*ceiling((n-1)/3)). - _Nathaniel Johnston_, Jan 10 2024
%t A240115 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 A240115 Table[schoenheim[n, 4, 2], {n, 4, 100}] (* _Jean-François Alcover_, Jan 26 2019, from PARI *)
%o A240115 (PARI) schoenheim(n, k, t) = {
%o A240115   my(lb = 1);
%o A240115   n += 1-t; k += 1-t;
%o A240115   while(t>0,
%o A240115     lb = ceil((lb*n)/k);
%o A240115     t--; n++; k++
%o A240115   );
%o A240115   lb
%o A240115 }
%o A240115 s=[]; for(n=4, 100, s=concat(s, schoenheim(n, 4, 2))); s
%Y A240115 Cf. A240116, A240117, A240118, A240119.
%Y A240115 Cf. A011975, A036831, A036832, A036833, A036834, A036835, A036836.
%K A240115 nonn,easy
%O A240115 4,2
%A A240115 _Colin Barker_, Apr 01 2014