A240118 - OEIS

A240118

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

1, 4, 5, 7, 11, 14, 18, 27, 32, 37, 54, 61, 68, 94, 103, 116, 147, 163, 180, 221, 240, 260, 319, 342, 366, 438, 465, 500, 581, 619, 658, 756, 800, 844, 968, 1016, 1066, 1210, 1265, 1329, 1485, 1555, 1627, 1805, 1882, 1960, 2173, 2257, 2343, 2582, 2673, 2778

(list; graph; refs; listen; history; text; internal format)

OFFSET

5,2

LINKS

Colin Barker, Table of n, a(n) for n = 5..1000

D. Gordon, G. Kuperberg and O. Patashnik, New constructions for covering designs, arXiv:math/9502238 [math.CO], 1995.

MATHEMATICA

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];

Table[schoenheim[n, 5, 3], {n, 5, 100}] (* Jean-François Alcover, Jan 26 2019, from PARI *)

PROG

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

my(lb = 1);

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

while(t>0,

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

t--; n++; k++

);

}

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

CROSSREFS