A169005 - OEIS

%I #10 Dec 28 2024 18:14:27

%S 1,40,1560,60840,2372760,92537640,3608967960,140749750440,

%T 5489240267160,214080370419240,8349134446350360,325616243407664040,

%U 12699033492898897560,495262306223057004840,19315229942699223188760

%N Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.

%C The initial terms coincide with those of A170759, although the two sequences are eventually different.

%C First disagreement at index 23: a(23) = 4031636291344199362636054396584348060, A170759(23) = 4031636291344199362636054396584348840. - Klaus Brockhaus, Apr 19 2011

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

%H <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, -741).

%F 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)/(741*t^23 - 38*t^22 - 38*t^21 - 38*t^20 - 38*t^19 - 38*t^18 - 38*t^17 - 38*t^16 - 38*t^15 - 38*t^14 - 38*t^13 - 38*t^12 - 38*t^11 - 38*t^10 - 38*t^9 - 38*t^8 - 38*t^7 - 38*t^6 - 38*t^5 - 38*t^4 - 38*t^3 - 38*t^2 - 38*t + 1).

%t coxG[{23,741,-38}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 28 2024 *)

%Y Cf. A170759 (G.f.: (1+x)/(1-39*x)).

%K nonn

%O 0,2

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