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A168752 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

%I A168752 #15 Nov 30 2022 13:33:38
%S A168752 1,27,702,18252,474552,12338352,320797152,8340725952,216858874752,
%T A168752 5638330743552,146596599332352,3811511582641152,99099301148669952,
%U A168752 2576581829865418752,66991127576500887552,1741769316989023076352
%N A168752 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.
%C A168752 The initial terms coincide with those of A170746, although the two sequences are eventually different.
%C A168752 First disagreement at index 18: a(18) = 30613337515399069589962401, A170746(18) = 30613337515399069589962752. - _Klaus Brockhaus_, Mar 26 2011
%C A168752 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168752 G. C. Greubel, <a href="/A168752/b168752.txt">Table of n, a(n) for n = 0..500</a>
%H A168752 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, -325).
%F A168752 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)/(325*t^18 - 25*t^17 - 25*t^16 - 25*t^15 - 25*t^14 - 25*t^13 - 25*t^12 - 25*t^11 - 25*t^10 - 25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1).
%t A168752 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)/(325*t^18 - 25*t^17 - 25*t^16 - 25*t^15 - 25*t^14 - 25*t^13 - 25*t^12 - 25*t^11 - 25*t^10 - 25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 10 2016 *)
%t A168752 coxG[{18,325,-25}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Nov 30 2022 *)
%Y A168752 Cf. A170746 (G.f.: (1+x)/(1-26*x)).
%K A168752 nonn,easy
%O A168752 0,2
%A A168752 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009