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A168745 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

%I A168745 #17 Nov 24 2016 13:55:36
%S A168745 1,20,380,7220,137180,2606420,49521980,940917620,17877434780,
%T A168745 339671260820,6453753955580,122621325156020,2329805177964380,
%U A168745 44266298381323220,841059669245141180,15980133715657682420
%N A168745 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.
%C A168745 The initial terms coincide with those of A170739, although the two sequences are eventually different.
%C A168745 First disagreement at index 18: a(18) = 109607737155696043718590, A170739(18) = 109607737155696043718780. - _Klaus Brockhaus_, Mar 27 2011
%C A168745 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168745 G. C. Greubel, <a href="/A168745/b168745.txt">Table of n, a(n) for n = 0..500</a>
%H A168745 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, -171).
%F A168745 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)/(171*t^18 - 18*t^17 - 18*t^16 - 18*t^15 - 18*t^14 - 18*t^13 -18*t^12 - 18*t^11 - 18*t^10 - 18*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5- 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1).
%t A168745 coxG[{18,171,-18}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 01 2015 *)
%t A168745 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)/(171*t^18 - 18*t^17 - 18*t^16 - 18*t^15 - 18*t^14 - 18*t^13 - 18*t^12 - 18*t^11 - 18*t^10 - 18*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 10 2016 *)
%Y A168745 Cf. A170739 (G.f.: (1+x)/(1-19*x)).
%K A168745 nonn,easy
%O A168745 0,2
%A A168745 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009