

A162367


Number of reduced words of length n in the Weyl group D_25.


31



1, 25, 324, 2900, 20149, 115805, 572975, 2507895, 9904050, 35818770, 120016066, 376029250, 1110031585, 3106677225, 8286768736, 21161266240, 51931463950, 122883804990, 281186004075, 623785796595, 1344621849285, 2822018693325
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OFFSET

0,2


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)*Product_{i=1..k1} f(2*i), where f(m) = (1x^m)/(1x) [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) (1x^m)/(1x) ; end proc:
g := proc(k, M) local a, i; global f;
a:=f(k)*mul(f(2*i), i=1..k1);
seriestolist(series(a, x, M+1));
end proc;


MATHEMATICA

f[m_] := (1x^m)/(1x);
With[{k = 25}, CoefficientList[f[k]*Product[f[2i], {i, 1, k1}] + O[x]^(k3), x]] (* JeanFrançois Alcover, Feb 15 2023, after Maple code *)


CROSSREFS

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


KEYWORD

nonn


AUTHOR



STATUS

approved



