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A169357 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169357 #19 May 10 2018 00:18:46
%S A169357 1,8,56,392,2744,19208,134456,941192,6588344,46118408,322828856,
%T A169357 2259801992,15818613944,110730297608,775112083256,5425784582792,
%U A169357 37980492079544,265863444556808,1861044111897656,13027308783283592
%N A169357 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169357 The initial terms coincide with those of A003950, although the two sequences are eventually different.
%C A169357 First disagreement at index 31: a(31) = 180314722325538064702905964, A003950(31) = 180314722325538064702905992. - _Klaus Brockhaus_, Jun 17 2011
%C A169357 Computed with Magma using commands similar to those used to compute A154638.
%H A169357 Vincenzo Librandi, <a href="/A169357/b169357.txt">Table of n, a(n) for n = 0..200</a>
%H A169357 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,-21).
%F A169357 G.f.: (t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*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)/(21*t^31 - 6*t^30 - 6*t^29 - 6*t^28 - 6*t^27 - 6*t^26 - 6*t^25 - 6*t^24 - 6*t^23 - 6*t^22 - 6*t^21 - 6*t^20 - 6*t^19 - 6*t^18 - 6*t^17 - 6*t^16 - 6*t^15 - 6*t^14 - 6*t^13 - 6*t^12 - 6*t^11 - 6*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1).
%t A169357 With[{num=Total[2t^Range[30]]+t^31+1,den=Total[-6 t^Range[30]]+21t^31+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Sep 17 2013 *)
%Y A169357 Cf. A003950 (G.f.: (1+x)/(1-7*x)).
%K A169357 nonn,easy
%O A169357 0,2
%A A169357 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009