

A162412


Number of reduced words of length n in the Weyl group D_43.


49



1, 43, 945, 14147, 162238, 1519706, 12107381, 84352455, 524443953, 2954877827, 15270874059, 73095540169, 326649986846, 1371916939730, 5445905213996, 20530576252412, 73812456221233, 253999791183699, 839265188017740
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OFFSET

0,2


COMMENTS

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


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

G.f. for D_m is the polynomial f(n) * Product( f(2i), i=1..n1 )/ f(1)^n, where f(k) = 1x^k. Only finitely many terms are nonzero. This is a row of the triangle in A162206.


CROSSREFS

Growth series for groups D_n, n = 3,...,50: 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, A162380, A162381, A162384, A162388, A162389, A162392, A162399, A162402, A162403, A162411, A162412, A162413, A162418, A162452, A162456, A162461, A162469, A162492; also A162206.


KEYWORD

nonn


AUTHOR



STATUS

approved



