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A162368
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Number of reduced words of length n in the Weyl group D_26.
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31
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1, 26, 350, 3250, 23399, 139204, 712179, 3220074, 13124124, 48942894, 168958960, 544988210, 1655019795, 4761697020, 13048465756, 34209731996, 86141195946, 209025000936, 490211005011, 1113996801606, 2458618650891, 5280637344216
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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 IV.)
J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
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LINKS
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Table of n, a(n) for n=0..21.
Index entries for growth series for groups
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FORMULA
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The growth series for D_k is the polynomial f(k)*Product_{i=1..k-1} f(2*i), where f(m) = (1-x^m)/(1-x) [Corrected by N. J. A. Sloane, Aug 07 2021]. This is a row of the triangle in A162206.
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MAPLE
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# Growth series for D_k, truncated to terms of order M. - N. J. A. Sloane, Aug 07 2021
f := proc(m::integer) (1-x^m)/(1-x) ; end proc:
g := proc(k, M) local a, i; global f;
a:=f(k)*mul(f(2*i), i=1..k-1);
seriestolist(series(a, x, M+1));
end proc;
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MATHEMATICA
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f[m_] := (1-x^m)/(1-x);
With[{k = 26}, CoefficientList[f[k]*Product[f[2i], {i, 1, k-1}] + O[x]^(k-4), x]] (* Jean-François Alcover, Feb 15 2023, after Maple code *)
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CROSSREFS
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Growth series for groups D_n, n = 3,...,32: A161435, A162207, A162208, A162209, A162210, A162211, A162212, A162248, A162288, A162297, A162300, A162301, A162321, A162327, A162328, A162346, A162347, A162359, A162360, A162364, A162365, A162366, A162367, A162368, A162369, A162370, A162376, A162377, A162378, A162379; also A162206
Sequence in context: A054938 A161526 A161933 * A225979 A162718 A010978
Adjacent sequences: A162365 A162366 A162367 * A162369 A162370 A162371
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KEYWORD
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nonn,changed
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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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