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A162288 Number of reduced words of length n in the Weyl group D_11. 32
1, 11, 65, 275, 934, 2706, 6941, 16159, 34749, 69927, 132991, 240900, 418187, 699193, 1130581, 1774058, 2709201, 4036252, 5878719, 8385597, 11733007, 16125043, 21793619, 28997122, 38017704, 49157086, 62730799, 79060850 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

N. Bourbaki, Groupes et Algèbres de Lie, Chap. 4, 5 and 6, Hermann, Paris, 1968. See Chap. VI, Section 4, Problem 10a, page 231, W(t).

J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.

LINKS

Table of n, a(n) for n=0..27.

Index entries for growth series for groups

FORMULA

The growth series for D_k is the polynomial f(k)*Prod_{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.

MAPLE

# 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;

MATHEMATICA

x = y + y O[y]^(n^2);

(1-x^n) Product[1-x^(2k), {k, 1, n-1}]/(1-x)^n // CoefficientList[#, y]& (* Jean-François Alcover, Mar 25 2020, from A162206 *)

x =.; n = 11; CoefficientList[ Product[1 - x^(2 k), {k, 1, n - 1}] (1 - x^n) /(1 - x)^n // Expand, x] (* Michael Somos, Aug 06 2021 *)

CROSSREFS

The growth series for D_k, k >= 3, are also the rows of the triangle A162206.

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: A184055 A332750 A161459 * A161776 A054333 A267173

Adjacent sequences:  A162285 A162286 A162287 * A162289 A162290 A162291

KEYWORD

nonn

AUTHOR

John Cannon and N. J. A. Sloane, Dec 01 2009

EXTENSIONS

Entry revised by N. J. A. Sloane, Jan 17 2016

STATUS

approved

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Last modified September 21 21:32 EDT 2021. Contains 347605 sequences. (Running on oeis4.)