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

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

Crossrefs

Cf. A240115, A240116, A240117, A240119.

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

Sequence in context: A080327 A283485 A184778 * A343211 A237133 A253584

Adjacent sequences: A240115 A240116 A240117 * A240119 A240120 A240121

Keyword

nonn

Author

Colin Barker, Apr 01 2014

Status

approved