# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a168823 Showing 1-1 of 1 %I A168823 #15 Apr 22 2019 15:36:40 %S A168823 1,50,2450,120050,5882450,288240050,14123762450,692064360050, %T A168823 33911153642450,1661646528480050,81420679895522450, %U A168823 3989613314880600050,195491052429149402450,9579061569028320720050,469374016882387715282450 %N A168823 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I. %C A168823 The initial terms coincide with those of A170769, although the two sequences are eventually different. %C A168823 First disagreement at index 19: a(19) = 132586542292982673588951169078825, A170769(19) = 132586542292982673588951169080050. - _Klaus Brockhaus_, Apr 01 2011 %C A168823 Computed with MAGMA using commands similar to those used to compute A154638. %H A168823 G. C. Greubel, Table of n, a(n) for n = 0..500 %H A168823 Index entries for linear recurrences with constant coefficients, signature (48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, -1176). %F A168823 G.f.: (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^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 A168823 CoefficientList[Series[(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^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,0,50}], t] (* _G. C. Greubel_, Nov 21 2016 *) %t A168823 coxG[{19,1176,-48}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 22 2019 *) %Y A168823 Cf. A170769 (G.f.: (1+x)/(1-49*x)). %K A168823 nonn,easy %O A168823 0,2 %A A168823 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE