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A170678 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

%I A170678 #8 Jan 23 2019 12:54:34
%S A170678 1,45,1980,87120,3833280,168664320,7421230080,326534123520,
%T A170678 14367501434880,632170063134720,27815482777927680,1223881242228817920,
%U A170678 53850774658067988480,2369434084954991493120,104255099738019625697280
%N A170678 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
%C A170678 The initial terms coincide with those of A170764, although the two sequences are eventually different.
%C A170678 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170678 <a href="/index/Rec#order_49">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, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, -946).
%F A170678 G.f. (t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 +
%F A170678 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170678 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A170678 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 A170678 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 A170678 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 A170678 1)/(946*t^49 - 43*t^48 - 43*t^47 - 43*t^46 - 43*t^45 - 43*t^44 - 43*t^43
%F A170678 - 43*t^42 - 43*t^41 - 43*t^40 - 43*t^39 - 43*t^38 - 43*t^37 - 43*t^36 -
%F A170678 43*t^35 - 43*t^34 - 43*t^33 - 43*t^32 - 43*t^31 - 43*t^30 - 43*t^29 -
%F A170678 43*t^28 - 43*t^27 - 43*t^26 - 43*t^25 - 43*t^24 - 43*t^23 - 43*t^22 -
%F A170678 43*t^21 - 43*t^20 - 43*t^19 - 43*t^18 - 43*t^17 - 43*t^16 - 43*t^15 -
%F A170678 43*t^14 - 43*t^13 - 43*t^12 - 43*t^11 - 43*t^10 - 43*t^9 - 43*t^8 -
%F A170678 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1)
%t A170678 coxG[{49,946,-43}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 23 2019 *)
%K A170678 nonn
%O A170678 0,2
%A A170678 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009