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A169204 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.

%I A169204 #12 Sep 30 2019 14:19:19
%S A169204 1,47,2162,99452,4574792,210440432,9680259872,445291954112,
%T A169204 20483429889152,942237774900992,43342937645445632,1993775131690499072,
%U A169204 91713656057762957312,4218828178657096036352,194066096218226417672192
%N A169204 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
%C A169204 The initial terms coincide with those of A170766, although the two sequences are eventually different.
%C A169204 First disagreement at index 27: a(27) = 801311695774083274277408250529829634978085831, A170766(27) = 801311695774083274277408250529829634978086912. - _Klaus Brockhaus_, May 07 2011
%C A169204 Computed with Magma using commands similar to those used to compute A154638.
%H A169204 <a href="/index/Rec#order_27">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, -1035).
%F A169204 G.f.: (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^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).
%t A169204 coxG[{27,1035,-45}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 30 2019 *)
%Y A169204 Cf. A170766 (G.f.: (1+x)/(1-46*x)).
%K A169204 nonn
%O A169204 0,2
%A A169204 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009