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A054653
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Acyclic orientations of the Hamming graph (K_3) x (K_n).
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1
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1, 6, 204, 19164, 3733056, 1288391040, 712770186240, 589563294888960, 692610802412175360, 1110893919113884631040, 2357555468242103997235200, 6453187419589244410090291200, 22305345996450386267133758668800
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OFFSET
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0,2
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COMMENTS
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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.
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REFERENCES
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M. Harborth, Structural analysis of shop scheduling problems, PhD thesis, Otto-von-Guericke-Univ. Magdeburg, GCA-Verlag, 1999 (in German)
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LINKS
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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.
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FORMULA
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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.
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A054652, A053870, A054583.
Sequence in context: A115491 A082405 A183595 * A061540 A173370 A159307
Adjacent sequences: A054650 A054651 A054652 * A054654 A054655 A054656
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KEYWORD
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nonn,easy
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AUTHOR
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M. Harborth (Martin.Harborth(AT)vt.siemens.de)
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STATUS
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approved
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