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 A167923 #18 Sep 11 2023 01:49:11 %S A167923 1,15,210,2940,41160,576240,8067360,112943040,1581202560,22136835840, %T A167923 309915701760,4338819824640,60743477544960,850408685629440, %U A167923 11905721598812160,166680102383370240,2333521433367183255 %N A167923 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I. %C A167923 The initial terms coincide with those of A170734, although the two sequences are eventually different. %C A167923 Computed with MAGMA using commands similar to those used to compute A154638. %H A167923 G. C. Greubel, <a href="/A167923/b167923.txt">Table of n, a(n) for n = 0..500</a> %H A167923 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,-91). %F A167923 G.f.: (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)/( 91*t^16 - 13*t^15 - 13*t^14 - 13*t^13 - 13*t^12 - 13*t^11 - 13*t^10 - 13*t^9 - 13*t^8 - 13*t^7 - 13*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1). %F A167923 From _G. C. Greubel_, Sep 10 2023: (Start) %F A167923 G.f.: (1+t)*(1-t^16)/(1 - 14*t + 104*t^16 - 91*t^17). %F A167923 a(n) = 13*Sum_{j=1..15} a(n-j) - 91*a(n-16). (End) %t A167923 CoefficientList[Series[(1+t)*(1-t^16)/(1-14*t+104*t^16-91*t^17), {t, 0, 50}], t] (* _G. C. Greubel_, Jul 01 2016; Sep 10 2023 *) %t A167923 coxG[{16,91,-13}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 22 2020 *) %o A167923 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-14*x+104*x^16-91*x^17) )); // _G. C. Greubel_, Sep 10 2023 %o A167923 (SageMath) %o A167923 def A167955_list(prec): %o A167923 P.<x> = PowerSeriesRing(ZZ, prec) %o A167923 return P( (1+x)*(1-x^16)/(1-14*x+104*x^16-91*x^17) ).list() %o A167923 A167955_list(40) # _G. C. Greubel_, Sep 10 2023 %Y A167923 Cf. A154638, A169452, A170734. %K A167923 nonn %O A167923 0,2 %A A167923 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009