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A133713 Array read by antidiagonals, giving the sizes pi_l(c_l(m,n)) of minimal covers (see reference for precise definition). 13
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
2,5
LINKS
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
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

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Last modified March 3 02:27 EST 2024. Contains 370499 sequences. (Running on oeis4.)