login
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).
12

%I #16 Feb 02 2020 21:04:45

%S 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 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 24,57,113,132,158,105,72,30,11,1,7,26,78,149,245,246

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

%D 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 J. Schoenheim, <a href="http://projecteuclid.org/euclid.pjm/1103033815">On coverings</a>, Pac. J. Math. 14 (4) (1964) 1405-1411.

%H <a href="/index/Cor#covnum">Index entries for covering numbers</a>

%e Triangle begins

%e 1;

%e 2, 1;

%e 2, 3, 1;

%e 3, 4, 4, 1;

%e 3, 6, 6, 5, 1;

%e 4, 7, 11, 9, 6, 1;

%e 4, 11, 14, 18, 12, 7, 1;

%e 5, 12, 25, 26, 27, 16, 8, 1;

%e ...

%p L := proc(v,k,t,l)

%p local i,t1;

%p t1 := l;

%p for i from v-t+1 to v do

%p t1 := ceil(t1*i/(i-(v-k)));

%p od:

%p t1;

%p end;

%p A036838 := proc(n,k)

%p L(n+2,k+2,k+1,1) ;

%p end proc:

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

%K nonn,tabl,easy,nice

%O 0,2

%A _N. J. A. Sloane_, Jan 11 2002