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A240118 Schoenheim lower bound L(n,5,3).

%I A240118 #14 Jan 26 2019 14:27:40
%S A240118 1,4,5,7,11,14,18,27,32,37,54,61,68,94,103,116,147,163,180,221,240,
%T A240118 260,319,342,366,438,465,500,581,619,658,756,800,844,968,1016,1066,
%U A240118 1210,1265,1329,1485,1555,1627,1805,1882,1960,2173,2257,2343,2582,2673,2778
%N A240118 Schoenheim lower bound L(n,5,3).
%H A240118 Colin Barker, <a href="/A240118/b240118.txt">Table of n, a(n) for n = 5..1000</a>
%H A240118 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.
%t A240118 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 A240118 Table[schoenheim[n, 5, 3], {n, 5, 100}] (* _Jean-François Alcover_, Jan 26 2019, from PARI *)
%o A240118 (PARI) schoenheim(n, k, t) = {
%o A240118   my(lb = 1);
%o A240118   n += 1-t; k += 1-t;
%o A240118   while(t>0,
%o A240118     lb = ceil((lb*n)/k);
%o A240118     t--; n++; k++
%o A240118   );
%o A240118   lb
%o A240118 }
%o A240118 s=[]; for(n=5, 100, s=concat(s, schoenheim(n, 5, 3))); s
%Y A240118 Cf. A240115, A240116, A240117, A240119.
%Y A240118 Cf. A011975, A036831, A036832, A036833, A036834, A036835, A036836.
%K A240118 nonn
%O A240118 5,2
%A A240118 _Colin Barker_, Apr 01 2014