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 A054653 Number of acyclic orientations of the Hamming graph (K_3) x (K_n). 1
 1, 6, 204, 19164, 3733056, 1288391040, 712770186240, 589563294888960, 692610802412175360, 1110893919113884631040, 2357555468242103997235200, 6453187419589244410090291200, 22305345996450386267133758668800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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. REFERENCES M. Harborth, Structural analysis of shop scheduling problems, PhD thesis, Otto-von-Guericke-Univ. Magdeburg, GCA-Verlag, 1999 (in German) LINKS Table of n, a(n) for n=0..12. M. Harborth, Structural analysis of shop scheduling problems, (PhD thesis in German with English abstract). K. B. Athreya, C. R. Pranesachar, and N. M. Singhi, On the number of Latin rectangles and chromatic polynomial of L(K_{r,s}), European J. Combin. 1 (1980) 9-17. FORMULA a(n) = (-1)^n*(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}]) with z=-1. MATHEMATICA 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}] CROSSREFS Cf. A054652, A053870, A054583. Sequence in context: A115491 A082405 A183595 * A061540 A173370 A159307 Adjacent sequences: A054650 A054651 A054652 * A054654 A054655 A054656 KEYWORD nonn,easy AUTHOR M. Harborth (Martin.Harborth(AT)vt.siemens.de) STATUS approved

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Last modified September 13 04:25 EDT 2024. Contains 375859 sequences. (Running on oeis4.)