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

%I #14 Jan 26 2019 14:27:40

%S 1,4,5,7,11,14,18,27,32,37,54,61,68,94,103,116,147,163,180,221,240,

%T 260,319,342,366,438,465,500,581,619,658,756,800,844,968,1016,1066,

%U 1210,1265,1329,1485,1555,1627,1805,1882,1960,2173,2257,2343,2582,2673,2778

%N Schoenheim lower bound L(n,5,3).

%H Colin Barker, <a href="/A240118/b240118.txt">Table of n, a(n) for n = 5..1000</a>

%H 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 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 Table[schoenheim[n, 5, 3], {n, 5, 100}] (* _Jean-François Alcover_, Jan 26 2019, from PARI *)

%o (PARI) schoenheim(n, k, t) = {

%o my(lb = 1);

%o n += 1-t; k += 1-t;

%o while(t>0,

%o lb = ceil((lb*n)/k);

%o t--; n++; k++

%o );

%o lb

%o }

%o s=[]; for(n=5, 100, s=concat(s, schoenheim(n, 5, 3))); s

%Y Cf. A240115, A240116, A240117, A240119.

%Y Cf. A011975, A036831, A036832, A036833, A036834, A036835, A036836.

%K nonn

%O 5,2

%A _Colin Barker_, Apr 01 2014