cp's OEIS Frontend

A169561 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

%I A169561 #12 Nov 26 2016 09:28:44
%S A169561 1,20,380,7220,137180,2606420,49521980,940917620,17877434780,
%T A169561 339671260820,6453753955580,122621325156020,2329805177964380,
%U A169561 44266298381323220,841059669245141180,15980133715657682420
%N A169561 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
%C A169561 The initial terms coincide with those of A170739, although the two sequences are eventually different.
%C A169561 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169561 <a href="/index/Rec#order_35">Index entries for linear recurrences with constant coefficients</a>, signature (18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, -171).
%F A169561 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 A169561 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 A169561 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 A169561 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 A169561 + 2*t^2 + 2*t + 1)/(171*t^35 - 18*t^34 - 18*t^33 - 18*t^32 - 18*t^31 -
%F A169561 18*t^30 - 18*t^29 - 18*t^28 - 18*t^27 - 18*t^26 - 18*t^25 - 18*t^24 -
%F A169561 18*t^23 - 18*t^22 - 18*t^21 - 18*t^20 - 18*t^19 - 18*t^18 - 18*t^17 -
%F A169561 18*t^16 - 18*t^15 - 18*t^14 - 18*t^13 - 18*t^12 - 18*t^11 - 18*t^10 -
%F A169561 18*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 -
%F A169561 18*t + 1)
%t A169561 With[{num=Total[2t^Range[34]]+t^35+1,den=Total[-18 t^Range[34]]+ 171t^35+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jun 20 2011 *)
%K A169561 nonn
%O A169561 0,2
%A A169561 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009