A240116 Schoenheim lower bound L(n,5,2).

1, 3, 3, 4, 4, 6, 7, 8, 8, 12, 12, 13, 14, 18, 19, 20, 21, 27, 28, 29, 30, 37, 38, 40, 41, 48, 50, 52, 53, 62, 63, 65, 67, 76, 78, 80, 82, 93, 95, 97, 99, 111, 113, 116, 118, 130, 133, 136, 138, 152, 154, 157, 160, 174, 177, 180, 183, 199, 202, 205, 208, 225

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.

Formula

Empirical g.f.: x^5*(x^24 -x^21 -x^20 +2*x^17 +x^14 +x^12 -x^10 +2*x^9 +x^6 -x^4 +x^3 +2*x +1) / ( -x^25 +x^24 +x^21 -x^20 +x^5 -x^4 -x +1).

a(n) = ceiling((n/5)*ceiling((n-1)/4)). - Nathaniel Johnston, Jan 10 2024

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

Crossrefs

Cf. A240115, A240117, A240118, A240119.

Cf. A011975, A011977, A036831, A036832, A036833, A036834, A036835, A036836.

Sequence in context: A145814 A198465 A292836 * A007768 A180018 A011371

Adjacent sequences: A240113 A240114 A240115 * A240117 A240118 A240119

Keyword

nonn,easy

Author

Colin Barker, Apr 01 2014

Status

approved