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A168822 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%I A168822 #13 Nov 24 2016 16:28:17
%S A168822 1,49,2352,112896,5419008,260112384,12485394432,599298932736,
%T A168822 28766348771328,1380784741023744,66277667569139712,
%U A168822 3181328043318706176,152703746079297896448,7329779811806299029504,351829430966702353416192
%N A168822 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
%C A168822 The initial terms coincide with those of A170768, although the two sequences are eventually different.
%C A168822 First disagreement at index 19: a(19) = 89647535069497835525384077048680, A170768(19) = 89647535069497835525384077049856. - _Klaus Brockhaus_, Apr 01 2011
%C A168822 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168822 G. C. Greubel, <a href="/A168822/b168822.txt">Table of n, a(n) for n = 0..500</a>
%H A168822 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, -1128).
%F A168822 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)/(1128*t^19 - 47*t^18 - 47*t^17 - 47*t^16 - 47*t^15 - 47*t^14 - 47*t^13 - 47*t^12 - 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).
%t A168822 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)/(1128*t^19 - 47*t^18 - 47*t^17 - 47*t^16 - 47*t^15 - 47*t^14 - 47*t^13 - 47*t^12 - 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Nov 21 2016 *)
%Y A168822 Cf. A170768 (G.f.: (1+x)/(1-48*x)).
%K A168822 nonn,easy
%O A168822 0,2
%A A168822 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009