cp's OEIS Frontend

A170181 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.

%I A170181 #9 Nov 22 2016 15:54:43
%S A170181 1,28,756,20412,551124,14880348,401769396,10847773692,292889889684,
%T A170181 7908027021468,213516729579636,5764951698650172,155653695863554644,
%U A170181 4202649788315975388,113471544284531335476,3063731695682346057852
%N A170181 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
%C A170181 The initial terms coincide with those of A170747, although the two sequences are eventually different.
%C A170181 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170181 <a href="/index/Rec#order_39">Index entries for linear recurrences with constant coefficients</a>, signature (26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, -351).
%F A170181 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 A170181 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 A170181 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 A170181 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 A170181 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(351*t^39 -
%F A170181 26*t^38 - 26*t^37 - 26*t^36 - 26*t^35 - 26*t^34 - 26*t^33 - 26*t^32 -
%F A170181 26*t^31 - 26*t^30 - 26*t^29 - 26*t^28 - 26*t^27 - 26*t^26 - 26*t^25 -
%F A170181 26*t^24 - 26*t^23 - 26*t^22 - 26*t^21 - 26*t^20 - 26*t^19 - 26*t^18 -
%F A170181 26*t^17 - 26*t^16 - 26*t^15 - 26*t^14 - 26*t^13 - 26*t^12 - 26*t^11 -
%F A170181 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 -
%F A170181 26*t^2 - 26*t + 1)
%t A170181 With[{num=Total[2t^Range[38]]+t^39+1,den=Total[-26 t^Range[38]]+ 351t^39+ 1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Nov 05 2011 *)
%K A170181 nonn
%O A170181 0,2
%A A170181 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009