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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).

%I A036838 #16 Feb 02 2020 21:04:45
%S A036838 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,
%T A036838 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,
%U A036838 24,57,113,132,158,105,72,30,11,1,7,26,78,149,245,246
%N 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).
%C A036838 The relation with Schoenheim's notation is L(v,k,t,l) = psi(k,t,l,v). - _R. J. Mathar_, Aug 12 2012
%D A036838 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.
%H A036838 J. Schoenheim, <a href="http://projecteuclid.org/euclid.pjm/1103033815">On coverings</a>, Pac. J. Math. 14 (4) (1964) 1405-1411.
%H A036838 <a href="/index/Cor#covnum">Index entries for covering numbers</a>
%e A036838 Triangle begins
%e A036838   1;
%e A036838   2,  1;
%e A036838   2,  3,  1;
%e A036838   3,  4,  4,  1;
%e A036838   3,  6,  6,  5,  1;
%e A036838   4,  7, 11,  9,  6,  1;
%e A036838   4, 11, 14, 18, 12,  7,  1;
%e A036838   5, 12, 25, 26, 27, 16,  8,  1;
%e A036838   ...
%p A036838 L := proc(v,k,t,l)
%p A036838     local i,t1;
%p A036838     t1 := l;
%p A036838     for i from v-t+1 to v do
%p A036838         t1 := ceil(t1*i/(i-(v-k)));
%p A036838     od:
%p A036838     t1;
%p A036838 end;
%p A036838 A036838 := proc(n,k)
%p A036838     L(n+2,k+2,k+1,1) ;
%p A036838 end proc:
%t A036838 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 *)
%Y A036838 Columns give A011975, A036831, A036832, A036833, A036834, A036835, A036836, A014125, A036830, A036837.
%K A036838 nonn,tabl,easy,nice
%O A036838 0,2
%A A036838 _N. J. A. Sloane_, Jan 11 2002