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A162494
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Number of reduced words of length n in the Weyl group E_8 on 8 generators and order 696729600.
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4
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1, 8, 35, 112, 294, 672, 1386, 2640, 4718, 8000, 12978, 20272, 30645, 45016, 64470, 90264, 123829, 166768, 220849, 287992, 370250, 469784, 588833, 729680, 894613, 1085880, 1305640, 1555912, 1838523, 2155056, 2506798, 2894688, 3319268, 3780640, 4278429
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OFFSET
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0,2
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REFERENCES
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N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche VII.)
H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, Table 10.
J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..120
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FORMULA
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G.f.: (1-x^2)*(1-x^8)*(1-x^12)*(1-x^14)*(1-x^18)*(1-x^20)*(1-x^24)*(1-x^30)/(1-x)^8.
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MATHEMATICA
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CoefficientList[Series[(1 - x^2) (1 - x^8) (1 - x^12) (1 - x^14) (1 - x^18) (1 - x^20) (1 - x^24) (1 - x^30) / (1 - x)^8, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 09 2013 *)
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PROG
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(Magma) G := CoxeterGroup(GrpFPCox, "E8");
f := GrowthFunction(G);
Coefficients(f);
(PARI) Vec((1-x^2)*(1-x^8)*(1-x^12)*(1-x^14)*(1-x^18)*(1-x^20)*(1-x^24)*(1-x^30)/(1-x)^8 + O(x^121)) \\ Jinyuan Wang, Mar 08 2020
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CROSSREFS
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Cf. A161409, A162493.
Sequence in context: A005732 A162211 A161717 * A040977 A266785 A267170
Adjacent sequences: A162491 A162492 A162493 * A162495 A162496 A162497
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KEYWORD
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nonn,fini,full
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AUTHOR
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John Cannon and N. J. A. Sloane, Dec 01 2009
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STATUS
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approved
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