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A168914 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.

%I A168914 #10 Jan 23 2019 19:55:53
%S A168914 1,45,1980,87120,3833280,168664320,7421230080,326534123520,
%T A168914 14367501434880,632170063134720,27815482777927680,1223881242228817920,
%U A168914 53850774658067988480,2369434084954991493120,104255099738019625697280
%N A168914 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
%C A168914 The initial terms coincide with those of A170764, although the two sequences are eventually different.
%C A168914 First disagreement at index 21: a(21) = 33286339890656766317672687122512930, A170764(21) = 33286339890656766317672687122513920. - Klaus Brockhaus, Apr 08 2011
%C A168914 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168914 <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, -946).
%F A168914 G.f.: (t^21 + 2*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)/(946*t^21 - 43*t^20 - 43*t^19 - 43*t^18 - 43*t^17 - 43*t^16 - 43*t^15 - 43*t^14 - 43*t^13 - 43*t^12 - 43*t^11 - 43*t^10 - 43*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).
%t A168914 coxG[{21,946,-43}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 23 2019 *)
%Y A168914 Cf. A170764 (G.f.: (1+x)/(1-44*x)).
%K A168914 nonn
%O A168914 0,2
%A A168914 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009