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A169394 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169394 #13 Oct 12 2024 01:40:37
%S A169394 1,45,1980,87120,3833280,168664320,7421230080,326534123520,
%T A169394 14367501434880,632170063134720,27815482777927680,1223881242228817920,
%U A169394 53850774658067988480,2369434084954991493120,104255099738019625697280
%N A169394 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169394 The initial terms coincide with those of A170764, although the two sequences are eventually different.
%C A169394 First disagreement at index 31: a(31) = 905300600325059075883780523727014801779401341008930, A170764(31) = 905300600325059075883780523727014801779401341009920. - _Klaus Brockhaus_, Jun 17 2011
%C A169394 Computed with Magma using commands similar to those used to compute A154638.
%H A169394 <a href="/index/Rec#order_31">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, -946).
%F A169394 G.f.: (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)/(946*t^31 - 43*t^30 - 43*t^29 - 43*t^28 - 43*t^27 - 43*t^26 - 43*t^25 - 43*t^24 - 43*t^23 - 43*t^22 - 43*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).
%Y A169394 Cf. A170764 (G.f.: (1+x)/(1-44*x)).
%K A169394 nonn
%O A169394 0,2
%A A169394 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009