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A169490 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.

%I A169490 #8 Nov 26 2016 07:27:59
%S A169490 1,45,1980,87120,3833280,168664320,7421230080,326534123520,
%T A169490 14367501434880,632170063134720,27815482777927680,1223881242228817920,
%U A169490 53850774658067988480,2369434084954991493120,104255099738019625697280
%N A169490 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
%C A169490 The initial terms coincide with those of A170764, although the two sequences are eventually different.
%C A169490 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169490 <a href="/index/Rec#order_33">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, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, -946).
%F A169490 G.f. (t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A169490 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +
%F A169490 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +
%F A169490 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 +
%F A169490 1)/(946*t^33 - 43*t^32 - 43*t^31 - 43*t^30 - 43*t^29 - 43*t^28 - 43*t^27
%F A169490 - 43*t^26 - 43*t^25 - 43*t^24 - 43*t^23 - 43*t^22 - 43*t^21 - 43*t^20 -
%F A169490 43*t^19 - 43*t^18 - 43*t^17 - 43*t^16 - 43*t^15 - 43*t^14 - 43*t^13 -
%F A169490 43*t^12 - 43*t^11 - 43*t^10 - 43*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5
%F A169490 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1)
%t A169490 coxG[{33,946,-43}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 25 2015 *)
%K A169490 nonn
%O A169490 0,2
%A A169490 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009