A240119 Schoenheim lower bound L(n,6,3).

1, 4, 4, 6, 7, 11, 14, 18, 19, 30, 32, 37, 42, 57, 64, 70, 77, 104, 112, 121, 130, 167, 178, 194, 205, 248, 267, 286, 301, 362, 378, 401, 425, 494, 520, 547, 574, 667, 697, 728, 759, 870, 904, 948, 984, 1105, 1153, 1202, 1242, 1394, 1438, 1492, 1547, 1711

Offset

6,2

Links

Colin Barker, Table of n, a(n) for n = 6..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, 6, 3], {n, 6, 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=6, 100, s=concat(s, schoenheim(n, 6, 3))); s

Crossrefs

Cf. A240115, A240116, A240117, A240118.

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

Sequence in context: A065677 A006672 A107287 * A292755 A294021 A200267

Adjacent sequences: A240116 A240117 A240118 * A240120 A240121 A240122

Keyword

nonn

Author

Colin Barker, Apr 01 2014

Status

approved