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A169114 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.

%I A169114 #13 Nov 25 2016 12:13:54
%S A169114 1,5,20,80,320,1280,5120,20480,81920,327680,1310720,5242880,20971520,
%T A169114 83886080,335544320,1342177280,5368709120,21474836480,85899345920,
%U A169114 343597383680,1374389534720,5497558138880,21990232555520,87960930222080
%N A169114 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
%C A169114 The initial terms coincide with those of A003947, although the two sequences are eventually different.
%C A169114 First disagreement at index 26: a(26) = 5629499534213110, A003947(26) = 5629499534213120. - Klaus Brockhaus, Apr 30 2011
%C A169114 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169114 Vincenzo Librandi, <a href="/A169114/b169114.txt">Table of n, a(n) for n = 0..1000</a>
%H A169114 <a href="/index/Rec#order_26">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, 3, 3, 3, 3, 3, 3, 3, -6).
%F A169114 G.f.: (t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*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^26 - 3*t^25 - 3*t^24 - 3*t^23 - 3*t^22 - 3*t^21 - 3*t^20 - 3*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 A169114 With[{num=Total[2t^Range[25]]+t^26+1,den=Total[-3 t^Range[25]]+6t^26+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Sep 27 2013 *)
%Y A169114 Cf. A003947 (G.f.: (1+x)/(1-4*x)).
%K A169114 nonn
%O A169114 0,2
%A A169114 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009