

A161698


Number of reduced words of length n in the Weyl group B_5.


0



1, 5, 14, 30, 54, 86, 125, 169, 215, 259, 297, 325, 340, 340, 325, 297, 259, 215, 169, 125, 86, 54, 30, 14, 5, 1
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OFFSET

0,2


COMMENTS

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


REFERENCES

J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under PoincarĂ© polynomial.
N. Bourbaki, Groupes et algĂ¨bres. de Lie, Chap. 4, 5, 6. (The group is defined in Planche II.)


LINKS

Table of n, a(n) for n=0..25.


FORMULA

G.f. for B_m is the polynomial Prod_{k=1..m}(1x^(2k))/(1x). Only finitely many terms are nonzero. This is a row of the triangle in A128084.


MAPLE

seq(coeff(series(mul((1x^(2*k))/(1x), k=1..5), x, n+1), x, n), n = 0 .. 25); # Muniru A Asiru, Oct 25 2018


MATHEMATICA

CoefficientList[Series[Product[(1x^(2*k)), {k, 1, 5}] /(1x)^5, {x, 0, 25}], x] (* G. C. Greubel, Oct 25 2018 *)


PROG

(PARI) t='t+O('t^26); Vec(prod(k=1, 5, 1t^(2*k))/(1t)^5) \\ G. C. Greubel, Oct 25 2018
(MAGMA) m:=26; R<t>:=PowerSeriesRing(Integers(), m); Coefficients(R!((&*[1t^(2*k): k in [1..5]])/(1t)^5)); // G. C. Greubel, Oct 25 2018


CROSSREFS

The growth series for the finite Coxeter (or Weyl) groups B_2 through B_12 are A161696A161699, A161716, A161717, A161733, A161755, A161776, A161858. These are all rows of A128084. The growth series for the affine Coxeter (or Weyl) groups B_2 through B_12 are A008576, A008137, A267167A267175.
Sequence in context: A231669 A256986 A162208 * A049791 A053461 A136135
Adjacent sequences: A161695 A161696 A161697 * A161699 A161700 A161701


KEYWORD

nonn,fini,full


AUTHOR

John Cannon and N. J. A. Sloane, Nov 30 2009


STATUS

approved



