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A240117
Schoenheim lower bound L(n,6,2).
5
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
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
KEYWORD
nonn
AUTHOR
Colin Barker, Apr 01 2014
STATUS
approved