A133713 Array read by antidiagonals, giving the sizes pi_l(c_l(m,n)) of minimal covers (see reference for precise definition).

1, 1, 1, 1, 3, 1, 1, 6, 7, 1, 1, 10, 25, 13, 1, 1, 15, 65, 81, 22, 1, 1, 21, 140, 325, 226, 34, 1, 1, 28, 266, 995, 1371, 561, 50, 1, 1, 36, 462, 2541, 5901, 5087, 1277, 70, 1, 1, 45, 750, 5698, 20097, 30569, 17080, 2706, 95, 1

Offset

2,5

Links

Table of n, a(n) for n=2..56.

A. P. Burger and J. H. van Vuuren, Balanced minimal covers of a finite set, Discr. Math. 307 (2007), 2853-2860.

Formula

Burger and van Vuuren give a generating function.

Example

Array begins:
1 1 1 1 1 1 1 1 1 ...
1 3 7 13 22 34 50 ...
1 6 25 81 226 561 1277 ...
1 10 65 325 1371 5087 17080 ...
1 15 140 995 5901 30569 142375 ...
...

Maple

A133713 := proc(l, cl)
        g := 1 ;
        for k from 1 to cl+1 do
          add( binomial(binomial(l, k+1)+i-1, i)*t^(i*k), i=0..ceil(cl/k)) ;
          g := g*% ;
        end do:
        g := expand(g) ;
        coeftayl(g, t=0, cl) ;
end proc:
seq(seq(A133713(d-k, k), k=0..d-2), d=2..11); # R. J. Mathar, Nov 23 2011

Mathematica

A133713[l_, cl_] := Module[{g, k, s}, g = 1; For[k = 1, k <= cl+1, k++, s = Sum[Binomial[Binomial[l, k+1]+i-1, i]*t^(i*k), {i, 0, Ceiling[cl/k]}]; g = g*s]; g = Expand[g]; SeriesCoefficient[g, {t, 0, cl}]]; A133713[_, 0] = 1; Table[A133713[l-cl+2, cl], {l, 0, 9}, {cl, 0, l}] // Flatten (* Jean-François Alcover, Jan 07 2014, translated from Maple *)

Crossrefs

Rows give A002623, A133714-A133717.

Columns give A000217, A001296, A133718-A133710.

Sequence in context: A245474 A338369 A339231 * A008278 A213735 A056858

Adjacent sequences: A133710 A133711 A133712 * A133714 A133715 A133716

Keyword

nonn,tabl

Author

N. J. A. Sloane, Dec 30 2007

Extensions

Missing term 2706 inserted by Jean-François Alcover, Jan 07 2014

Status

approved