cp's OEIS Frontend

A170424 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.

%I A170424 #8 Nov 21 2016 17:30:41
%S A170424 1,31,930,27900,837000,25110000,753300000,22599000000,677970000000,
%T A170424 20339100000000,610173000000000,18305190000000000,549155700000000000,
%U A170424 16474671000000000000,494240130000000000000,14827203900000000000000
%N A170424 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
%C A170424 The initial terms coincide with those of A170750, although the two sequences are eventually different.
%C A170424 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170424 <a href="/index/Rec#order_44">Index entries for linear recurrences with constant coefficients</a>, signature (29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, -435).
%F A170424 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 A170424 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 A170424 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 A170424 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 A170424 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 A170424 + 2*t^3 + 2*t^2 + 2*t + 1)/(435*t^44 - 29*t^43 - 29*t^42 - 29*t^41 -
%F A170424 29*t^40 - 29*t^39 - 29*t^38 - 29*t^37 - 29*t^36 - 29*t^35 - 29*t^34 -
%F A170424 29*t^33 - 29*t^32 - 29*t^31 - 29*t^30 - 29*t^29 - 29*t^28 - 29*t^27 -
%F A170424 29*t^26 - 29*t^25 - 29*t^24 - 29*t^23 - 29*t^22 - 29*t^21 - 29*t^20 -
%F A170424 29*t^19 - 29*t^18 - 29*t^17 - 29*t^16 - 29*t^15 - 29*t^14 - 29*t^13 -
%F A170424 29*t^12 - 29*t^11 - 29*t^10 - 29*t^9 - 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5
%F A170424 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1)
%t A170424 With[{num=Total[2t^Range[43]]+t^44+1,den=Total[-29 t^Range[43]]+ 435t^44+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Sep 24 2012 *)
%K A170424 nonn
%O A170424 0,2
%A A170424 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009