Search: id:A054653
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%I A054653
%S A054653 1,6,204,19164,3733056,1288391040,712770186240,589563294888960,
%T A054653 692610802412175360,1110893919113884631040,2357555468242103997235200,
%U A054653 6453187419589244410090291200,22305345996450386267133758668800
%N A054653 Acyclic orientations of the Hamming graph (K_3) x (K_n).
%C A054653 This number is equivalent to the number of plans (i.e. structural solutions) 
               of the open shop problem with n jobs and 3 machines - see problems 
               in scheduling theory.
%D A054653 K.B. Athreya, C.R. Pranesachar, N.M. Singhi, On the number of Latin rectangles 
               and chromatic polynomial of L(K_{r,s}), European J. Combin. 1 (1980) 
               9-17
%D A054653 M. Harborth, Structural analysis of shop scheduling problems, PhD thesis, 
               Otto-von-Guericke-Univ. Magdeburg, GCA-Verlag, 1999 (in German)
%H A054653 <a href="http://www.math.uni-magdeburg.de/publ/diss/sources/harborth_diss.ps.gz">
               Structural analysis of shop scheduling problems (PhD thesis in German 
               with English abstract)</a>
%F A054653 (-1)^n*(z!n!/(((z-n)!)^3)*Sum[If[a+b+c*n, (-1)^b*2^c*((z-n+a)!)^2/(a!c!)*Bino 
               mial[3z-3n+3a+b+2, b], 0], {c, 0, n}, {b, 0, n}, {a, 0, n}]) with 
               z=-1
%t A054653 Table[n!*Evaluate[(-1)^n*FunctionExpand[z!n!/(((z-n)!)^3)*Sum[If[a+b+c*n, 
               (-1 )^b*2^c*((z-n+a)!)^2/(a!c!)*Binomial[3z-3n+3a+b+2, b], 0], {c, 
               0, n}, {b, 0, n}, {a, 0, n}]]/.z->-1]/n!, {n, 0, 15}]
%Y A054653 Cf. A054652, A053870, A054583.
%Y A054653 Sequence in context: A003743 A115491 A082405 this_sequence A061540 A159307 
               A024083
%Y A054653 Adjacent sequences: A054650 A054651 A054652 this_sequence A054654 A054655 
               A054656
%K A054653 nonn,easy
%O A054653 0,2
%A A054653 M. Harborth (Martin.Harborth(AT)vt.siemens.de)

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