A168754 - OEIS

%I #15 Nov 24 2016 13:58:18

%S 1,29,812,22736,636608,17825024,499100672,13974818816,391294926848,

%T 10956257951744,306775222648832,8589706234167296,240511774556684288,

%U 6734329687587160064,188561231252440481792,5279714475068333490176

%N Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

%C The initial terms coincide with those of A170748, although the two sequences are eventually different.

%C First disagreement at index 18: a(18) = 115900292156700056776343146, A170748(18) = 115900292156700056776343552. - _Klaus Brockhaus_, Mar 26 2011

%C Computed with MAGMA using commands similar to those used to compute A154638.

%H G. C. Greubel, <a href="/A168754/b168754.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, -378).

%F 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)/(378*t^18 - 27*t^17 - 27*t^16 - 27*t^15 - 27*t^14 - 27*t^13 - 27*t^12 - 27*t^11 - 27*t^10 - 27*t^9 - 27*t^8 - 27*t^7 - 27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).

%t With[{num=Total[2t^Range[17]]+t^18+1,den=Total[-27 t^Range[17]]+ 378t^18+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Feb 21 2013 *)

%t 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)/(378*t^18 - 27*t^17 - 27*t^16 - 27*t^15 - 27*t^14 - 27*t^13 - 27*t^12 - 27*t^11 - 27*t^10 - 27*t^9 - 27*t^8 - 27*t^7 - 27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 10 2016 *)

%Y Cf. A170748 (G.f.: (1+x)/(1-28*x)).

%K nonn,easy

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009