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A168771 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

%I A168771 #15 Jan 20 2025 11:18:25
%S A168771 1,46,2070,93150,4191750,188628750,8488293750,381973218750,
%T A168771 17188794843750,773495767968750,34807309558593750,1566328930136718750,
%U A168771 70484801856152343750,3171816083526855468750,142731723758708496093750
%N A168771 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.
%C A168771 The initial terms coincide with those of A170765, although the two sequences are eventually different.
%C A168771 First disagreement at index 18: a(18) = 585289274738054026794433592715, A170765(18) = 585289274738054026794433593750. - _Klaus Brockhaus_, Mar 26 2011
%C A168771 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168771 G. C. Greubel, <a href="/A168771/b168771.txt">Table of n, a(n) for n = 0..500</a>
%H A168771 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, -990).
%F A168771 G.f.: (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)/(990*t^18 - 44*t^17 - 44*t^16 - 44*t^15 - 44*t^14 - 44*t^13 - 44*t^12 - 44*t^11 - 44*t^10 - 44*t^9 - 44*t^8 - 44*t^7 - 44*t^6 - 44*t^5 - 44*t^4 - 44*t^3 - 44*t^2 - 44*t + 1).
%t A168771 CoefficientList[Series[(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)/(990*t^18 - 44*t^17 - 44*t^16 - 44*t^15 - 44*t^14 - 44*t^13 - 44*t^12 - 44*t^11 - 44*t^10 - 44*t^9 - 44*t^8 - 44*t^7 - 44*t^6 - 44*t^5 - 44*t^4 - 44*t^3 - 44*t^2 - 44*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 12 2016 *)
%t A168771 coxG[{18,990,-44}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 20 2025 *)
%Y A168771 Cf. A170765 (G.f.: (1+x)/(1-45*x)).
%K A168771 nonn
%O A168771 0,2
%A A168771 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009