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A036838
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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).
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12
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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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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The relation with Schoenheim's notation is L(v,k,t,l) = psi(k,t,l,v). - R. J. Mathar, Aug 12 2012
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REFERENCES
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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.
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LINKS
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J. Schoenheim, On coverings, Pac. J. Math. 14 (4) (1964) 1405-1411.
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EXAMPLE
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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;
...
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MAPLE
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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;
L(n+2, k+2, k+1, 1) ;
end proc:
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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