A169155 - OEIS

%I #10 Nov 25 2016 12:25:29

%S 1,46,2070,93150,4191750,188628750,8488293750,381973218750,

%T 17188794843750,773495767968750,34807309558593750,1566328930136718750,

%U 70484801856152343750,3171816083526855468750,142731723758708496093750

%N Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.

%C The initial terms coincide with those of A170765, although the two sequences are eventually different.

%C First disagreement at index 26: a(26) = 9841712544508343661854104399681091308592715, A170765(26) = 9841712544508343661854104399681091308593750. - Klaus Brockhaus, Apr 30 2011

%C Computed with MAGMA using commands similar to those used to compute A154638.

%H <a href="/index/Rec#order_26">Index entries for linear recurrences with constant coefficients</a>, signature (44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, -990).

%F G.f.: (t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 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 + 2*t^2 + 2*t + 1)/(990*t^26 - 44*t^25 - 44*t^24 - 44*t^23 - 44*t^22 - 44*t^21 - 44*t^20 - 44*t^19 - 44*t^18 - 44*t^17 - 44*t^16 - 44*t^15 - 44*t^14 - 44*t^13 - 44*t^12 - 44*t^11 - 44*t^10 - 44*t^9 - 44*t^8 - 44*t^7 - 44*t^6 - 44*t^5 - 44*t^4 - 44*t^3 - 44*t^2 - 44*t + 1).

%t With[{num=Total[2t^Range[25]]+t^26+1,den=Total[-44 t^Range[25]]+ 990t^26+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jan 24 2013 *)

%Y Cf. A170765 (G.f.: (1+x)/(1-45*x)).

%K nonn

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009