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A162248 Number of reduced words of length n in the Weyl group D_10.

%I A162248 #37 Mar 17 2025 17:20:46
%S A162248 1,10,54,210,659,1772,4235,9218,18590,35178,63063,107900,177243,
%T A162248 280850,430939,642364,932680,1322068,1833095,2490290,3319525,4347200,
%U A162248 5599243,7099950,8870703,10928616,13285169,15944898,18904214,22150426,25661040,29403398,33334708,37402498
%N A162248 Number of reduced words of length n in the Weyl group D_10.
%D A162248 N. Bourbaki, Groupes et Algèbres de Lie, Chap. 4, 5 and 6, Hermann, Paris, 1968. See Chap. VI, Section 4, Problem 10a, page 231, W(t).
%D A162248 J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
%H A162248 Andrew Howroyd, <a href="/A162248/b162248.txt">Table of n, a(n) for n = 0..90</a>
%H A162248 <a href="/index/Gre#GROWTH">Index entries for growth series for groups</a>
%F A162248 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 A162248 # Growth series for D_k, truncated to terms of order M. - _N. J. A. Sloane_, Aug 07 2021
%p A162248 f := proc(m::integer) (1-x^m)/(1-x) ; end proc:
%p A162248 g := proc(k,M) local a,i; global f;
%p A162248 a:=f(k)*mul(f(2*i),i=1..k-1);
%p A162248 seriestolist(series(a,x,M+1));
%p A162248 end proc;
%t A162248 x = y + y O[y]^(n^2);
%t A162248 (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 A162248 Row 10 of A162206.
%Y A162248 Growth series for groups D_n, n = 3,...,50: A161435, A162207, A162208, A162209, A162210, A162211, A162212, 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.
%K A162248 nonn,fini,full
%O A162248 0,2
%A A162248 _John Cannon_ and _N. J. A. Sloane_, Dec 01 2009
%E A162248 Entry revised by _N. J. A. Sloane_, Jan 17 2016
%E A162248 Data corrected by _Jean-François Alcover_, Mar 25 2020