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A240115
Schoenheim lower bound L(n,4,2).
6
1, 3, 3, 4, 6, 7, 8, 11, 12, 13, 18, 19, 20, 26, 27, 29, 35, 37, 39, 46, 48, 50, 59, 61, 63, 73, 75, 78, 88, 91, 94, 105, 108, 111, 124, 127, 130, 144, 147, 151, 165, 169, 173, 188, 192, 196, 213, 217, 221, 239, 243, 248, 266, 271, 276, 295, 300, 305, 326
OFFSET
4,2
COMMENTS
Only differs from A011976 when n = 7, 9, 10, or 19. - Nathaniel Johnston, Jan 10 2024
LINKS
D. Gordon, G. Kuperberg and O. Patashnik, New constructions for covering designs, arXiv:math/9502238 [math.CO], 1995.
FORMULA
Empirical g.f.: x^4*(x^15 -x^13 -x^12 +2*x^10 +x^7 +x^5 +2*x +1) / ( -x^16 +x^15 +x^13 -x^12 +x^4 -x^3 -x +1).
a(n) = ceiling((n/4)*ceiling((n-1)/3)). - 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, 4, 2], {n, 4, 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=4, 100, s=concat(s, schoenheim(n, 4, 2))); s
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Apr 01 2014
STATUS
approved