A240117 Schoenheim lower bound L(n,6,2).

1, 3, 3, 3, 4, 4, 6, 7, 7, 8, 8, 12, 12, 13, 14, 14, 19, 20, 20, 21, 22, 27, 28, 29, 30, 31, 38, 39, 40, 41, 42, 50, 51, 52, 54, 55, 63, 65, 66, 68, 69, 79, 80, 82, 84, 85, 96, 98, 99, 101, 103, 114, 116, 118, 120, 122, 135, 137, 139, 141, 143, 157, 159, 161

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.

Formula

Empirical g.f.: x^6*(x^35 -x^31 -x^30 +2*x^26 +x^23 +x^20 -x^18 +x^17 +x^16 +x^13 -x^12 +2*x^11 +x^7 -x^5 +x^4 +2*x +1) / ( -x^36 +x^35 +x^31 -x^30 +x^6 -x^5 -x +1).

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, 2], {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, 2))); s

Crossrefs

Cf. A240115, A240116, A240118, A240119.

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

Sequence in context: A177018 A156349 A237526 * A333536 A069941 A002036

Adjacent sequences: A240114 A240115 A240116 * A240118 A240119 A240120

Keyword

nonn

Author

Colin Barker, Apr 01 2014

Status

approved