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A168768 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

%I A168768 #16 Nov 24 2016 14:02:34
%S A168768 1,43,1806,75852,3185784,133802928,5619722976,236028364992,
%T A168768 9913191329664,416354035845888,17486869505527296,734448519232146432,
%U A168768 30846837807750150144,1295567187925506306048,54413821892871264854016
%N A168768 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.
%C A168768 The initial terms coincide with those of A170762, although the two sequences are eventually different.
%C A168768 First disagreement at index 18: a(18) = 169319271928759943361182170233, A170762(18) = 169319271928759943361182171136. - _Klaus Brockhaus_, Mar 26 2011
%C A168768 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168768 G. C. Greubel, <a href="/A168768/b168768.txt">Table of n, a(n) for n = 0..500</a>
%H A168768 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, -861).
%F A168768 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)/(861*t^18 - 41*t^17 - 41*t^16 - 41*t^15 - 41*t^14 - 41*t^13 - 41*t^12 - 41*t^11 - 41*t^10 - 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).
%t A168768 coxG[{18,861,-41}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 22 2016 *)
%t A168768 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)/(861*t^18 - 41*t^17 - 41*t^16 - 41*t^15 - 41*t^14 - 41*t^13 - 41*t^12 - 41*t^11 - 41*t^10 - 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 11 2016 *)
%Y A168768 Cf. A170762 (G.f.: (1+x)/(1-42*x)).
%K A168768 nonn,easy
%O A168768 0,2
%A A168768 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009