cp's OEIS Frontend

A168841 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

%I A168841 #10 Sep 06 2023 14:03:28
%S A168841 1,20,380,7220,137180,2606420,49521980,940917620,17877434780,
%T A168841 339671260820,6453753955580,122621325156020,2329805177964380,
%U A168841 44266298381323220,841059669245141180,15980133715657682420
%N A168841 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
%C A168841 The initial terms coincide with those of A170739, although the two sequences are eventually different.
%C A168841 First disagreement at index 20: a(20) = 39568393113206271782479390, A170739(20) = 39568393113206271782479580. - Klaus Brockhaus, Apr 02 2011
%C A168841 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168841 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, -171).
%F A168841 G.f.: (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)/(171*t^20 - 18*t^19 - 18*t^18 - 18*t^17 - 18*t^16 - 18*t^15 - 18*t^14 - 18*t^13 - 18*t^12 - 18*t^11 - 18*t^10 - 18*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1).
%t A168841 coxG[{20,171,-18}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 06 2023 *)
%Y A168841 Cf. A170739 (G.f.: (1+x)/(1-19*x)).
%K A168841 nonn
%O A168841 0,2
%A A168841 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009