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A169109 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.

%I A169109 #12 Jan 25 2025 15:31:54
%S A169109 1,48,2256,106032,4983504,234224688,11008560336,517402335792,
%T A169109 24317909782224,1142941759764528,53718262708932816,
%U A169109 2524758347319842352,118663642324032590544,5577191189229531755568,262127985893787992511696
%N A169109 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
%C A169109 The initial terms coincide with those of A170767, although the two sequences are eventually different.
%C A169109 First disagreement at index 25: a(25) = 648022115858739972719828904323294335394760, A170767(25) = 648022115858739972719828904323294335395888. - Klaus Brockhaus, Apr 25 2011
%C A169109 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169109 <a href="/index/Rec#order_25">Index entries for linear recurrences with constant coefficients</a>, signature (46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, -1081).
%F A169109 G.f.: (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)/(1081*t^25 - 46*t^24 - 46*t^23 - 46*t^22 - 46*t^21 - 46*t^20 - 46*t^19 - 46*t^18 - 46*t^17 - 46*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).
%t A169109 With[{num=Total[2t^Range[24]]+t^25+1,den=Total[-46 t^Range[24]]+1081t^25+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Apr 01 2014 *)
%t A169109 coxG[{25,1081,-46}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 25 2025 *)
%Y A169109 Cf. A170767 (G.f.: (1+x)/(1-47*x)).
%K A169109 nonn
%O A169109 0,2
%A A169109 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009