cp's OEIS Frontend

A170196 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.

%I A170196 #8 Nov 22 2016 16:02:46
%S A170196 1,43,1806,75852,3185784,133802928,5619722976,236028364992,
%T A170196 9913191329664,416354035845888,17486869505527296,734448519232146432,
%U A170196 30846837807750150144,1295567187925506306048,54413821892871264854016
%N A170196 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
%C A170196 The initial terms coincide with those of A170762, although the two sequences are eventually different.
%C A170196 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170196 <a href="/index/Rec#order_39">Index entries for linear recurrences with constant coefficients</a>, signature (41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, -861).
%F A170196 G.f. (t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 +
%F A170196 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 +
%F A170196 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 +
%F A170196 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 +
%F A170196 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(861*t^39 -
%F A170196 41*t^38 - 41*t^37 - 41*t^36 - 41*t^35 - 41*t^34 - 41*t^33 - 41*t^32 -
%F A170196 41*t^31 - 41*t^30 - 41*t^29 - 41*t^28 - 41*t^27 - 41*t^26 - 41*t^25 -
%F A170196 41*t^24 - 41*t^23 - 41*t^22 - 41*t^21 - 41*t^20 - 41*t^19 - 41*t^18 -
%F A170196 41*t^17 - 41*t^16 - 41*t^15 - 41*t^14 - 41*t^13 - 41*t^12 - 41*t^11 -
%F A170196 41*t^10 - 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 -
%F A170196 41*t^2 - 41*t + 1)
%t A170196 With[{num=Total[2t^Range[38]]+t^39+1,den=Total[-41 t^Range[38]]+861t^39+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Jul 31 2014 *)
%K A170196 nonn
%O A170196 0,2
%A A170196 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009