The OEIS is supported by the many generous donors to the OEIS Foundation.


(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A162369 Number of reduced words of length n in the Weyl group D_27. 31
1, 27, 377, 3627, 27026, 166230, 878409, 4098483, 17222607, 66165501, 235124461, 780112671, 2435132466, 7196829486, 20245295242, 54455027238, 140596223184, 349621224120, 839832229131, 1953829030737, 4412447681628, 9693085025844 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=0..21.

Index entries for growth series for groups


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.


# 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;


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: A257786 A161530 A161954 * A231858 A341564 A162726

Adjacent sequences:  A162366 A162367 A162368 * A162370 A162371 A162372




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



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 4 23:17 EDT 2022. Contains 355086 sequences. (Running on oeis4.)