cp's OEIS Frontend

A170373 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

%I A170373 #8 Nov 21 2016 19:26:55
%S A170373 1,28,756,20412,551124,14880348,401769396,10847773692,292889889684,
%T A170373 7908027021468,213516729579636,5764951698650172,155653695863554644,
%U A170373 4202649788315975388,113471544284531335476,3063731695682346057852
%N A170373 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
%C A170373 The initial terms coincide with those of A170747, although the two sequences are eventually different.
%C A170373 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170373 <a href="/index/Rec#order_43">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, 26, 26, 26, 26, -351).
%F A170373 G.f. (t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 +
%F A170373 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A170373 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 +
%F A170373 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 +
%F A170373 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3
%F A170373 + 2*t^2 + 2*t + 1)/(351*t^43 - 26*t^42 - 26*t^41 - 26*t^40 - 26*t^39 -
%F A170373 26*t^38 - 26*t^37 - 26*t^36 - 26*t^35 - 26*t^34 - 26*t^33 - 26*t^32 -
%F A170373 26*t^31 - 26*t^30 - 26*t^29 - 26*t^28 - 26*t^27 - 26*t^26 - 26*t^25 -
%F A170373 26*t^24 - 26*t^23 - 26*t^22 - 26*t^21 - 26*t^20 - 26*t^19 - 26*t^18 -
%F A170373 26*t^17 - 26*t^16 - 26*t^15 - 26*t^14 - 26*t^13 - 26*t^12 - 26*t^11 -
%F A170373 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 A170373 26*t^2 - 26*t + 1)
%t A170373 With[{num=Total[2t^Range[42]]+t^43+1,den=Total[-26 t^Range[42]]+351t^43+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, May 04 2014 *)
%K A170373 nonn
%O A170373 0,2
%A A170373 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009