cp's OEIS Frontend

A170434 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.

%I A170434 #9 Nov 21 2016 17:36:03
%S A170434 1,41,1640,65600,2624000,104960000,4198400000,167936000000,
%T A170434 6717440000000,268697600000000,10747904000000000,429916160000000000,
%U A170434 17196646400000000000,687865856000000000000,27514634240000000000000
%N A170434 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
%C A170434 The initial terms coincide with those of A170760, although the two sequences are eventually different.
%C A170434 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170434 <a href="/index/Rec#order_44">Index entries for linear recurrences with constant coefficients</a>, signature (39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, -780).
%F A170434 G.f. (t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 +
%F A170434 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170434 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170434 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170434 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
%F A170434 + 2*t^3 + 2*t^2 + 2*t + 1)/(780*t^44 - 39*t^43 - 39*t^42 - 39*t^41 -
%F A170434 39*t^40 - 39*t^39 - 39*t^38 - 39*t^37 - 39*t^36 - 39*t^35 - 39*t^34 -
%F A170434 39*t^33 - 39*t^32 - 39*t^31 - 39*t^30 - 39*t^29 - 39*t^28 - 39*t^27 -
%F A170434 39*t^26 - 39*t^25 - 39*t^24 - 39*t^23 - 39*t^22 - 39*t^21 - 39*t^20 -
%F A170434 39*t^19 - 39*t^18 - 39*t^17 - 39*t^16 - 39*t^15 - 39*t^14 - 39*t^13 -
%F A170434 39*t^12 - 39*t^11 - 39*t^10 - 39*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5
%F A170434 - 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1)
%t A170434 With[{num=Total[2t^Range[43]]+t^44+1,den=Total[-39 t^Range[43]]+ 780t^44+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Oct 21 2011 *)
%K A170434 nonn
%O A170434 0,2
%A A170434 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009