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A168793 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%I A168793 #12 Nov 24 2016 16:19:14
%S A168793 1,20,380,7220,137180,2606420,49521980,940917620,17877434780,
%T A168793 339671260820,6453753955580,122621325156020,2329805177964380,
%U A168793 44266298381323220,841059669245141180,15980133715657682420
%N A168793 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
%C A168793 The initial terms coincide with those of A170739, although the two sequences are eventually different.
%C A168793 First disagreement at index 19: a(19) = 2082547005958224830656630, A170739(19) = 2082547005958224830656820. - _Klaus Brockhaus_, Mar 30 2011
%C A168793 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168793 G. C. Greubel, <a href="/A168793/b168793.txt">Table of n, a(n) for n = 0..500</a>
%H A168793 <a href="/index/Rec#order_19">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, 18, -171).
%F A168793 G.f.: (t^19 + 2*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^19 - 18*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 A168793 CoefficientList[Series[(t^19 + 2*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^19 - 18*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 15 2016 *)
%Y A168793 Cf. A170739 (G.f.: (1+x)/(1-19*x)).
%K A168793 nonn
%O A168793 0,2
%A A168793 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009