# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a168729 Showing 1-1 of 1 %I A168729 #14 Nov 24 2016 13:23:50 %S A168729 1,4,12,36,108,324,972,2916,8748,26244,78732,236196,708588,2125764, %T A168729 6377292,19131876,57395628,172186884,516560646,1549681920,4649045712, %U A168729 13947136992,41841410544,125524230336,376572687120,1129718049696 %N A168729 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I. %C A168729 The initial terms coincide with those of A003946, although the two sequences are eventually different. %C A168729 First disagreement at index 18: a(18) = 516560646, A003946(18) = 516560652. - _Klaus Brockhaus_, Mar 27 2011 %C A168729 Computed with MAGMA using commands similar to those used to compute A154638. %H A168729 G. C. Greubel, Table of n, a(n) for n = 0..500 %H A168729 Index entries for linear recurrences with constant coefficients, signature (2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -3). %F A168729 G.f.: (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)/(3*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). %t A168729 CoefficientList[Series[(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)/(3*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), {t,0,50}], t] (* _G. C. Greubel_, Aug 06 2016 *) %t A168729 coxG[{18,3,-2,30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 07 2016 *) %Y A168729 Cf. A003946 (G.f.: (1+x)/(1-3*x)). %K A168729 nonn,easy %O A168729 0,2 %A A168729 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE