cp's OEIS Frontend

A169008 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.

%I A169008 #10 Jul 07 2019 10:55:46
%S A169008 1,43,1806,75852,3185784,133802928,5619722976,236028364992,
%T A169008 9913191329664,416354035845888,17486869505527296,734448519232146432,
%U A169008 30846837807750150144,1295567187925506306048,54413821892871264854016
%N A169008 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
%C A169008 The initial terms coincide with those of A170762, although the two sequences are eventually different.
%C A169008 First disagreement at index 23: a(23) = 22128544249712653230123118922198678649, A170762(23) = 22128544249712653230123118922198679552. - Klaus Brockhaus, Apr 19 2011
%C A169008 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169008 <a href="/index/Rec#order_23">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, 41, 41, 41, 41, 41, 41, -861).
%F A169008 G.f.: (t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*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)/(861*t^23 - 41*t^22 - 41*t^21 - 41*t^20 - 41*t^19 - 41*t^18 - 41*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 A169008 coxG[{23,861,-41}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 07 2019 *)
%Y A169008 Cf. A170762 (G.f.: (1+x)/(1-42*x)).
%K A169008 nonn
%O A169008 0,2
%A A169008 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009