cp's OEIS Frontend

A170227 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.

%I A170227 #9 Nov 22 2016 15:23:00
%S A170227 1,26,650,16250,406250,10156250,253906250,6347656250,158691406250,
%T A170227 3967285156250,99182128906250,2479553222656250,61988830566406250,
%U A170227 1549720764160156250,38743019104003906250,968575477600097656250
%N A170227 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
%C A170227 The initial terms coincide with those of A170745, although the two sequences are eventually different.
%C A170227 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170227 <a href="/index/Rec#order_40">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, 24, 24, 24, 24, 24, -300).
%F A170227 G.f. (t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 +
%F A170227 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 +
%F A170227 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 +
%F A170227 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 +
%F A170227 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170227 1)/(300*t^40 - 24*t^39 - 24*t^38 - 24*t^37 - 24*t^36 - 24*t^35 - 24*t^34
%F A170227 - 24*t^33 - 24*t^32 - 24*t^31 - 24*t^30 - 24*t^29 - 24*t^28 - 24*t^27 -
%F A170227 24*t^26 - 24*t^25 - 24*t^24 - 24*t^23 - 24*t^22 - 24*t^21 - 24*t^20 -
%F A170227 24*t^19 - 24*t^18 - 24*t^17 - 24*t^16 - 24*t^15 - 24*t^14 - 24*t^13 -
%F A170227 24*t^12 - 24*t^11 - 24*t^10 - 24*t^9 - 24*t^8 - 24*t^7 - 24*t^6 - 24*t^5
%F A170227 - 24*t^4 - 24*t^3 - 24*t^2 - 24*t + 1)
%t A170227 With[{num=Total[2t^Range[39]]+t^40+1,den=Total[-24 t^Range[39]]+ 300t^40+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, May 04 2012 *)
%K A170227 nonn
%O A170227 0,2
%A A170227 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009