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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A162365 Number of reduced words of length n in the Weyl group D_23. 31
1, 23, 275, 2277, 14673, 78407, 361514, 1477750, 5461235, 18518565, 58282576, 171815888, 477989151, 1262643305, 3183445871, 7694405993, 17895700206, 40182143330, 87349858045, 184297593435, 378236260170, 756560791350 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Differs from A161930 first at index n=23. - R. J. Mathar, Jul 12 2010
REFERENCES
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.
LINKS
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 *)
CROSSREFS
Sequence in context: A142027 A161523 A161930 * A162680 A010975 A022588
KEYWORD
nonn,changed
AUTHOR
John Cannon and N. J. A. Sloane, Dec 01 2009
STATUS
approved

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 February 26 13:58 EST 2024. Contains 370352 sequences. (Running on oeis4.)