A169177 - OEIS

%I #10 Jun 12 2017 18:25:03

%S 1,20,380,7220,137180,2606420,49521980,940917620,17877434780,

%T 339671260820,6453753955580,122621325156020,2329805177964380,

%U 44266298381323220,841059669245141180,15980133715657682420

%N Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.

%C The initial terms coincide with those of A170739, although the two sequences are eventually different.

%C First disagreement at index 27: a(27) = 35369068361537314023911651906589430, A170739(27) = 35369068361537314023911651906589620. - Klaus Brockhaus, May 07 2011

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

%H <a href="/index/Rec#order_27">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, 18, 18, 18, 18, 18, 18, 18, -171).

%F G.f.: (t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*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)/(171*t^27 - 18*t^26 - 18*t^25 - 18*t^24 - 18*t^23 - 18*t^22 - 18*t^21 - 18*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 coxG[{27,171,-18}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 12 2017 *)

%Y Cf. A170739 (G.f.: (1+x)/(1-19*x)).

%K nonn

%O 0,2

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