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A162297 Number of reduced words of length n in the Weyl group D_12. 10
1, 12, 77, 352, 1286, 3992, 10933, 27092, 61841, 131768, 264759, 505660, 923857, 1623104, 2753895, 4528612, 7239585, 11280072, 17168009, 25572196, 37340381, 53528488, 75430016, 104604424, 142903123, 192491532, 255865533, 335860592 (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.

FORMULA

The growth series for the finite Coxeter group of type D_k (k >= 3) has G.f. = Prod_i (1-x^{m_i})/(1-x) where the m_i are [1,3,5,...,2k-3,k-1].

MATHEMATICA

n = 12;

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 *)

PROG

Computed with MAGMA using commands similar to those used to compute A161409.

CROSSREFS

The growth series for D_k, k >= 5, are A162208-A162212, A162248, A162288, A162297.

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

Sequence in context: A335253 A071767 A161461 * A161858 A054334 A267174

Adjacent sequences:  A162294 A162295 A162296 * A162298 A162299 A162300

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 June 6 03:48 EDT 2020. Contains 334858 sequences. (Running on oeis4.)