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A169566 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

%I A169566 #13 Nov 26 2016 09:30:17
%S A169566 1,25,600,14400,345600,8294400,199065600,4777574400,114661785600,
%T A169566 2751882854400,66045188505600,1585084524134400,38042028579225600,
%U A169566 913008685901414400,21912208461633945600,525893003079214694400
%N A169566 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
%C A169566 The initial terms coincide with those of A170744, although the two sequences are eventually different.
%C A169566 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169566 Vincenzo Librandi, <a href="/A169566/b169566.txt">Table of n, a(n) for n = 0..200</a>
%H A169566 <a href="/index/Rec#order_35">Index entries for linear recurrences with constant coefficients</a>, signature (23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, -276).
%F A169566 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 + 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)/(276*t^35 - 23*t^34 - 23*t^33 - 23*t^32 - 23*t^31 - 23*t^30 - 23*t^29 - 23*t^28 - 23*t^27 - 23*t^26 - 23*t^25 - 23*t^24 - 23*t^23 - 23*t^22 - 23*t^21 - 23*t^20 - 23*t^19 - 23*t^18 - 23*t^17 - 23*t^16 - 23*t^15 - 23*t^14 - 23*t^13 - 23*t^12 - 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1)
%t A169566 With[{num=Total[2t^Range[34]]+t^35+1,den=Total[-23 t^Range[34]]+ 276t^35+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jan 14 2012 *)
%K A169566 nonn
%O A169566 0,2
%A A169566 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009