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A168832 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

%I A168832 #14 Nov 24 2016 18:31:34
%S A168832 1,11,110,1100,11000,110000,1100000,11000000,110000000,1100000000,
%T A168832 11000000000,110000000000,1100000000000,11000000000000,
%U A168832 110000000000000,1100000000000000,11000000000000000,110000000000000000
%N A168832 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
%C A168832 The initial terms coincide with those of A003953, although the two sequences are eventually different.
%C A168832 First disagreement at index 20: a(20) = 109999999999999999945, A003953(20) = 110000000000000000000. - _Klaus Brockhaus_, Apr 01 2011
%C A168832 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168832 G. C. Greubel, <a href="/A168832/b168832.txt">Table of n, a(n) for n = 0..994</a>
%H A168832 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, -45).
%F A168832 G.f.: (t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(45*t^20 - 9*t^19 - 9*t^18 - 9*t^17 - 9*t^16 - 9*t^15 - 9*t^14 - 9*t^13 - 9*t^12 - 9*t^11 - 9*t^10 - 9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).
%t A168832 coxG[{20,45,-9}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 19 2015 *)
%t A168832 CoefficientList[Series[(t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(45*t^20 - 9*t^19 - 9*t^18 - 9*t^17 - 9*t^16 - 9*t^15 - 9*t^14 - 9*t^13 - 9*t^12 - 9*t^11 - 9*t^10 - 9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1), {t,0,100}], t] (* _G. C. Greubel_, Nov 22 2016 *)
%Y A168832 Cf. A003953 (G.f.: (1+x)/(1-10*x)).
%K A168832 nonn
%O A168832 0,2
%A A168832 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009