cp's OEIS Frontend

A170202 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.

%I A170202 #9 Nov 22 2016 16:06:12
%S A170202 1,49,2352,112896,5419008,260112384,12485394432,599298932736,
%T A170202 28766348771328,1380784741023744,66277667569139712,
%U A170202 3181328043318706176,152703746079297896448,7329779811806299029504,351829430966702353416192
%N A170202 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
%C A170202 The initial terms coincide with those of A170768, although the two sequences are eventually different.
%C A170202 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170202 <a href="/index/Rec#order_39">Index entries for linear recurrences with constant coefficients</a>, signature (47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, -1128).
%F A170202 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 A170202 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 A170202 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 A170202 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 A170202 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1128*t^39 -
%F A170202 47*t^38 - 47*t^37 - 47*t^36 - 47*t^35 - 47*t^34 - 47*t^33 - 47*t^32 -
%F A170202 47*t^31 - 47*t^30 - 47*t^29 - 47*t^28 - 47*t^27 - 47*t^26 - 47*t^25 -
%F A170202 47*t^24 - 47*t^23 - 47*t^22 - 47*t^21 - 47*t^20 - 47*t^19 - 47*t^18 -
%F A170202 47*t^17 - 47*t^16 - 47*t^15 - 47*t^14 - 47*t^13 - 47*t^12 - 47*t^11 -
%F A170202 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 -
%F A170202 47*t^2 - 47*t + 1)
%t A170202 With[{num=Total[2t^Range[38]]+t^39+1,den=Total[-47 t^Range[38]]+ 1128t^39+1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Mar 15 2012 *)
%K A170202 nonn
%O A170202 0,2
%A A170202 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009