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A168778 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%I A168778 #18 Nov 24 2016 16:14:44
%S A168778 1,5,20,80,320,1280,5120,20480,81920,327680,1310720,5242880,20971520,
%T A168778 83886080,335544320,1342177280,5368709120,21474836480,85899345920,
%U A168778 343597383670,1374389534640,5497558138410,21990232553040,87960930209760
%N A168778 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
%C A168778 The initial terms coincide with those of A003947, although the two sequences are eventually different.
%C A168778 First divergence is at a(19) = 343597383670, A003947(19) = 343597383680.
%C A168778 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168778 G. C. Greubel, <a href="/A168778/b168778.txt">Table of n, a(n) for n = 0..500</a>
%H A168778 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -6).
%F A168778 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)/(6*t^19 - 3*t^18 - 3*t^17 - 3*t^16 - 3*t^15 - 3*t^14 - 3*t^13 - 3*t^12 - 3*t^11 - 3*t^10 - 3*t^9 - 3*t^8 - 3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1).
%t A168778 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)/(6*t^19 - 3*t^18 - 3*t^17 - 3*t^16 - 3*t^15 - 3*t^14 - 3*t^13 - 3*t^12 - 3*t^11 - 3*t^10 - 3*t^9 - 3*t^8 - 3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 12 2016 *)
%Y A168778 Cf. A003947 (G.f.: (1+x)/(1-4*x)).
%K A168778 nonn,easy
%O A168778 0,2
%A A168778 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009