cp's OEIS Frontend

A169543 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.

%I A169543 #8 Jun 20 2021 18:34:41
%S A169543 1,50,2450,120050,5882450,288240050,14123762450,692064360050,
%T A169543 33911153642450,1661646528480050,81420679895522450,
%U A169543 3989613314880600050,195491052429149402450,9579061569028320720050,469374016882387715282450
%N A169543 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
%C A169543 The initial terms coincide with those of A170769, although the two sequences are eventually different.
%C A169543 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169543 <a href="/index/Rec#order_34">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, 48, 48, -1176).
%F A169543 G.f. (t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A169543 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A169543 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A169543 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 +
%F A169543 2*t + 1)/(1176*t^34 - 48*t^33 - 48*t^32 - 48*t^31 - 48*t^30 - 48*t^29 -
%F A169543 48*t^28 - 48*t^27 - 48*t^26 - 48*t^25 - 48*t^24 - 48*t^23 - 48*t^22 -
%F A169543 48*t^21 - 48*t^20 - 48*t^19 - 48*t^18 - 48*t^17 - 48*t^16 - 48*t^15 -
%F A169543 48*t^14 - 48*t^13 - 48*t^12 - 48*t^11 - 48*t^10 - 48*t^9 - 48*t^8 -
%F A169543 48*t^7 - 48*t^6 - 48*t^5 - 48*t^4 - 48*t^3 - 48*t^2 - 48*t + 1)
%t A169543 coxG[{34,1176,-48}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 20 2021 *)
%K A169543 nonn
%O A169543 0,2
%A A169543 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009