cp's OEIS Frontend

A170085 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.

%I A170085 #8 Nov 26 2016 10:05:08
%S A170085 1,28,756,20412,551124,14880348,401769396,10847773692,292889889684,
%T A170085 7908027021468,213516729579636,5764951698650172,155653695863554644,
%U A170085 4202649788315975388,113471544284531335476,3063731695682346057852
%N A170085 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
%C A170085 The initial terms coincide with those of A170747, although the two sequences are eventually different.
%C A170085 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170085 <a href="/index/Rec#order_37">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, -351).
%F A170085 G.f. (t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 +
%F A170085 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 +
%F A170085 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 +
%F A170085 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 +
%F A170085 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(351*t^37 - 26*t^36 - 26*t^35 -
%F A170085 26*t^34 - 26*t^33 - 26*t^32 - 26*t^31 - 26*t^30 - 26*t^29 - 26*t^28 -
%F A170085 26*t^27 - 26*t^26 - 26*t^25 - 26*t^24 - 26*t^23 - 26*t^22 - 26*t^21 -
%F A170085 26*t^20 - 26*t^19 - 26*t^18 - 26*t^17 - 26*t^16 - 26*t^15 - 26*t^14 -
%F A170085 26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 -
%F A170085 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1)
%t A170085 With[{num=Total[2t^Range[36]]+t^37+1,den=Total[-26 t^Range[36]]+351t^37+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Mar 07 2013 *)
%K A170085 nonn
%O A170085 0,2
%A A170085 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009