This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A165180 #11 Sep 04 2022 08:35:36 %S A165180 1,48,2256,106032,4983504,234224688,11008560336,517402335792, %T A165180 24317909781096,1142941759658496,53718262701458688, %U A165180 2524758346851499008,118663642296518664960,5577191187677793197568,262127985808702829674752 %N A165180 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I. %C A165180 The initial terms coincide with those of A170767, although the two sequences are eventually different. %C A165180 Computed with MAGMA using commands similar to those used to compute A154638. %H A165180 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (46, 46, 46, 46, 46, 46, 46, -1081). %F A165180 G.f.: (t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1081*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1). %F A165180 a(n) = -1081*a(n-8) + 46*Sum_{k=1..7} a(n-k). - _Wesley Ivan Hurt_, Sep 04 2022 %t A165180 With[{num=Total[2t^Range[7]]+t^8+1,den=Total[-46 t^Range[7]]+1081t^8+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jul 27 2011 *) %K A165180 nonn %O A165180 0,2 %A A165180 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009