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A162301 Number of reduced words of length n in the Weyl group D_14.

%I A162301 #19 Mar 17 2025 16:35:09
%S A162301 1,14,104,546,2274,7994,24647,68392,173978,411332,913445,1921218,
%T A162301 3852849,7407596,13716314,24553984,42632448,71994624,118534456,
%U A162301 190669584,300196001,463355582,702148097,1045918928,1533251980,2214194008,3152831605,4430235278,6147776297
%N A162301 Number of reduced words of length n in the Weyl group D_14.
%D A162301 N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche IV.)
%D A162301 J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
%H A162301 Andrew Howroyd, <a href="/A162301/b162301.txt">Table of n, a(n) for n = 0..182</a>
%H A162301 <a href="/index/Gre#GROWTH">Index entries for growth series for groups</a>
%F A162301 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.
%p A162301 # Growth series for D_k, truncated to terms of order M. - _N. J. A. Sloane_, Aug 07 2021
%p A162301 f := proc(m::integer) (1-x^m)/(1-x) ; end proc:
%p A162301 g := proc(k,M) local a,i; global f;
%p A162301 a:=f(k)*mul(f(2*i),i=1..k-1);
%p A162301 seriestolist(series(a,x,M+1));
%p A162301 end proc;
%t A162301 n = 14;
%t A162301 x = y + y O[y]^(n^2);
%t A162301 (1-x^n) Product[1-x^(2k), {k, 1, n-1}]/(1-x)^n // CoefficientList[#, y]& (* _Jean-François Alcover_, Mar 25 2020, from A162206 *)
%Y A162301 Row 14 of A162206
%Y A162301 Growth series for groups D_n, n = 3,...,50: A161435, A162207, A162208, A162209, A162210, A162211, A162212, A162248, A162288, A162297, A162300, 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.
%K A162301 nonn,fini,full
%O A162301 0,2
%A A162301 _John Cannon_ and _N. J. A. Sloane_, Dec 01 2009