cp's OEIS Frontend

A169567 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

%I A169567 #8 Nov 26 2016 09:30:34
%S A169567 1,26,650,16250,406250,10156250,253906250,6347656250,158691406250,
%T A169567 3967285156250,99182128906250,2479553222656250,61988830566406250,
%U A169567 1549720764160156250,38743019104003906250,968575477600097656250
%N A169567 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
%C A169567 The initial terms coincide with those of A170745, although the two sequences are eventually different.
%C A169567 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169567 <a href="/index/Rec#order_35">Index entries for linear recurrences with constant coefficients</a>, signature (24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, -300).
%F A169567 G.f. (t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A169567 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 A169567 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 A169567 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 A169567 + 2*t^2 + 2*t + 1)/(300*t^35 - 24*t^34 - 24*t^33 - 24*t^32 - 24*t^31 -
%F A169567 24*t^30 - 24*t^29 - 24*t^28 - 24*t^27 - 24*t^26 - 24*t^25 - 24*t^24 -
%F A169567 24*t^23 - 24*t^22 - 24*t^21 - 24*t^20 - 24*t^19 - 24*t^18 - 24*t^17 -
%F A169567 24*t^16 - 24*t^15 - 24*t^14 - 24*t^13 - 24*t^12 - 24*t^11 - 24*t^10 -
%F A169567 24*t^9 - 24*t^8 - 24*t^7 - 24*t^6 - 24*t^5 - 24*t^4 - 24*t^3 - 24*t^2 -
%F A169567 24*t + 1)
%t A169567 With[{num=Total[2t^Range[34]]+t^35+1,den=Total[-24 t^Range[34]]+300t^35+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, May 11 2013 *)
%K A169567 nonn
%O A169567 0,2
%A A169567 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009