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A169444 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169444 #18 Nov 16 2018 13:51:23
%S A169444 1,47,2162,99452,4574792,210440432,9680259872,445291954112,
%T A169444 20483429889152,942237774900992,43342937645445632,1993775131690499072,
%U A169444 91713656057762957312,4218828178657096036352,194066096218226417672192
%N A169444 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169444 The initial terms coincide with those of A170766, although the two sequences are eventually different.
%C A169444 First disagreement is at index 32, the difference is 1081. - _Klaus Brockhaus_, Jun 30 2011
%C A169444 Computed with Magma using commands similar to those used to compute A154638.
%H A169444 <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, signature (45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, -1035).
%F A169444 G.f.: (t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*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)/(1035*t^32 - 45*t^31 - 45*t^30 - 45*t^29 - 45*t^28 - 45*t^27 - 45*t^26 - 45*t^25 - 45*t^24 - 45*t^23 - 45*t^22 - 45*t^21 - 45*t^20 - 45*t^19 - 45*t^18 - 45*t^17 - 45*t^16 - 45*t^15 - 45*t^14 - 45*t^13 - 45*t^12 - 45*t^11 - 45*t^10 - 45*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1).
%F A169444 G.f.: (1+2*sum(k=1..31,x^k)+x^32)/(1-45*sum(k=1..31,x^k)+1035*x^32).
%t A169444 coxG[{32,1035,-45}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Nov 16 2018 *)
%Y A169444 Cf. A170766 (G.f.: (1+x)/(1-46*x) ).
%K A169444 nonn
%O A169444 0,2
%A A169444 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009