cp's OEIS Frontend

A168720 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

%I A168720 #12 Nov 24 2016 13:13:58
%S A168720 1,43,1806,75852,3185784,133802928,5619722976,236028364992,
%T A168720 9913191329664,416354035845888,17486869505527296,734448519232146432,
%U A168720 30846837807750150144,1295567187925506306048,54413821892871264854016
%N A168720 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.
%C A168720 The initial terms coincide with those of A170762, although the two sequences are eventually different.
%C A168720 First disagreement at index 17: a(17) = 4031411236399046270504336505, A170762(17) = 4031411236399046270504337408. - _Klaus Brockhaus_, Mar 28 2011
%C A168720 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168720 G. C. Greubel, <a href="/A168720/b168720.txt">Table of n, a(n) for n = 0..500</a>
%H A168720 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, -861).
%F A168720 G.f.: (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)/(861*t^17 - 41*t^16 - 41*t^15 - 41*t^14 - 41*t^13 - 41*t^12 - 41*t^11 - 41*t^10 - 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).
%t A168720 CoefficientList[Series[(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)/(861*t^17 - 41*t^16 - 41*t^15 - 41*t^14 - 41*t^13 - 41*t^12 - 41*t^11 - 41*t^10 - 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Aug 05 2016 *)
%Y A168720 Cf. A170762 (G.f.: (1+x)/(1-42*x)).
%K A168720 nonn
%O A168720 0,2
%A A168720 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009