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A162300 Number of reduced words of length n in the Weyl group D_13. 1
1, 13, 90, 442, 1728, 5720, 16653, 43745, 105586, 237354, 502113, 1007773, 1931631, 3554746, 6308706, 10837593, 18078112, 29360890, 46535840, 72124195, 109499325, 163097740, 238660747, 343506072, 486827392, 680018170, 937014482, 1274649714 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..27.

FORMULA

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

MATHEMATICA

n = 13;

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: A152867 A026912 A161465 * A161859 A057788 A267175

Adjacent sequences:  A162297 A162298 A162299 * A162301 A162302 A162303

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified August 5 14:14 EDT 2021. Contains 346469 sequences. (Running on oeis4.)