cp's OEIS Frontend

A169399 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169399 #15 Oct 12 2024 01:41:07
%S A169399 1,50,2450,120050,5882450,288240050,14123762450,692064360050,
%T A169399 33911153642450,1661646528480050,81420679895522450,
%U A169399 3989613314880600050,195491052429149402450,9579061569028320720050,469374016882387715282450
%N A169399 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169399 The initial terms coincide with those of A170769, although the two sequences are eventually different.
%C A169399 First disagreement at index 31: a(31) = 25401093036981168266109409882610825088621726241798825, A170769(31) = 25401093036981168266109409882610825088621726241800050. - _Klaus Brockhaus_, Jun 17 2011
%C A169399 Computed with Magma using commands similar to those used to compute A154638.
%H A169399 <a href="/index/Rec#order_31">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, -1176).
%F A169399 G.f.: (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^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).
%t A169399 coxG[{31,1176,-48}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Mar 06 2023 *)
%Y A169399 Cf. A170769 (G.f.: (1+x)/(1-49*x)).
%K A169399 nonn
%O A169399 0,2
%A A169399 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009