cp's OEIS Frontend

A169571 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

%I A169571 #8 Nov 26 2016 09:31:38
%S A169571 1,30,870,25230,731670,21218430,615334470,17844699630,517496289270,
%T A169571 15007392388830,435214379276070,12621216999006030,366015292971174870,
%U A169571 10614443496164071230,307818861388758065670,8926746980273983904430
%N A169571 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
%C A169571 The initial terms coincide with those of A170749, although the two sequences are eventually different.
%C A169571 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169571 <a href="/index/Rec#order_35">Index entries for linear recurrences with constant coefficients</a>, signature (28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, -406).
%F A169571 G.f. (t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A169571 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 +
%F A169571 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 +
%F A169571 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
%F A169571 + 2*t^2 + 2*t + 1)/(406*t^35 - 28*t^34 - 28*t^33 - 28*t^32 - 28*t^31 -
%F A169571 28*t^30 - 28*t^29 - 28*t^28 - 28*t^27 - 28*t^26 - 28*t^25 - 28*t^24 -
%F A169571 28*t^23 - 28*t^22 - 28*t^21 - 28*t^20 - 28*t^19 - 28*t^18 - 28*t^17 -
%F A169571 28*t^16 - 28*t^15 - 28*t^14 - 28*t^13 - 28*t^12 - 28*t^11 - 28*t^10 -
%F A169571 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 -
%F A169571 28*t + 1)
%t A169571 With[{num=Total[2t^Range[34]]+t^35+1,den=Total[-28 t^Range[34]]+406t^35+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, May 30 2013 *)
%K A169571 nonn
%O A169571 0,2
%A A169571 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009