A036838 Triangle read by rows: T(n,k) = value of Schoenheim bound L_1(n+2,k+2,k+1) on covering numbers (0 <= k <= n).

1, 2, 1, 2, 3, 1, 3, 4, 4, 1, 3, 6, 6, 5, 1, 4, 7, 11, 9, 6, 1, 4, 11, 14, 18, 12, 7, 1, 5, 12, 25, 26, 27, 16, 8, 1, 5, 17, 30, 50, 44, 39, 20, 9, 1, 6, 19, 47, 66, 92, 70, 54, 25, 10, 1, 6, 24, 57, 113, 132, 158, 105, 72, 30, 11, 1, 7, 26, 78, 149, 245, 246

Offset: 0

Author

N. J. A. Sloane, Jan 11 2002

Keywords

• nonn
• tabl
• easy
• nice

Comments

The relation with Schoenheim's notation is L(v,k,t,l) = psi(k,t,l,v). - R. J. Mathar, Aug 12 2012

Examples

			Triangle begins
  1;
  2,  1;
  2,  3,  1;
  3,  4,  4,  1;
  3,  6,  6,  5,  1;
  4,  7, 11,  9,  6,  1;
  4, 11, 14, 18, 12,  7,  1;
  5, 12, 25, 26, 27, 16,  8,  1;
  ...
		

References

• W. H. Mills and R. C. Mullin, Coverings and packings, pp. 371-399 of Jeffrey H. Dinitz and D. R. Stinson, editors, Contemporary Design Theory, Wiley, 1992. See Eq. 1.

Links

• J. Schoenheim, On coverings, Pac. J. Math. 14 (4) (1964) 1405-1411.
• Index entries for covering numbers

Crossrefs

Columns give A011975, A036831, A036832, A036833, A036834, A036835, A036836, A014125, A036830, A036837.

Programs

Maple

L := proc(v,k,t,l)
    local i,t1;
    t1 := l;
    for i from v-t+1 to v do
        t1 := ceil(t1*i/(i-(v-k)));
    od:
    t1;
end;
A036838 := proc(n,k)
    L(n+2,k+2,k+1,1) ;
end proc:

Mathematica

L[v_, k_, t_, l_] := Module[{i, t1}, t1 = l; For[i = v-t+1, i <= v, i++, t1 = Ceiling[t1*i/(i-(v-k))]]; t1]; A036838[n_, k_] := L[n+2, k+2, k+1, 1]; Table[A036838[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, Sep 16 2013, translated from Maple *)