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A169447 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169447 #16 May 08 2018 01:11:04
%S A169447 1,50,2450,120050,5882450,288240050,14123762450,692064360050,
%T A169447 33911153642450,1661646528480050,81420679895522450,
%U A169447 3989613314880600050,195491052429149402450,9579061569028320720050,469374016882387715282450
%N A169447 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169447 The initial terms coincide with those of A170769, although the two sequences are eventually different.
%C A169447 First disagreement is at index 32, the difference is 1225. - _Klaus Brockhaus_, Jun 30 2011
%C A169447 Computed with Magma using commands similar to those used to compute A154638.
%H A169447 <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, signature (48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, -1176).
%F A169447 G.f.: (t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*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)/(1176*t^32 - 48*t^31 - 48*t^30 - 48*t^29 - 48*t^28 - 48*t^27 - 48*t^26 - 48*t^25 - 48*t^24 - 48*t^23 - 48*t^22 - 48*t^21 - 48*t^20 - 48*t^19 - 48*t^18 - 48*t^17 - 48*t^16 - 48*t^15 - 48*t^14 - 48*t^13 - 48*t^12 - 48*t^11 - 48*t^10 - 48*t^9 - 48*t^8 - 48*t^7 - 48*t^6 - 48*t^5 - 48*t^4 - 48*t^3 - 48*t^2 - 48*t + 1).
%F A169447 G.f.: (1+2*sum(k=1..31,x^k)+x^32)/(1-48*sum(k=1..31,x^k)+1176*x^32).
%t A169447 coxG[{32,1176,-48}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 25 2017 *)
%Y A169447 Cf. A170769 (G.f.: (1+x)/(1-49*x) ).
%K A169447 nonn
%O A169447 0,2
%A A169447 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009