A169197 - OEIS

%I #12 Feb 16 2025 18:01:40

%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)^27 = I.

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

%C First disagreement at index 27: a(27) = 9326952693483615917696116319288492564757660, A170759(27) = 9326952693483615917696116319288492564758440. - _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 (38, 38, 38, 38, 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^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)/(741*t^27 - 38*t^26 - 38*t^25 - 38*t^24 - 38*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[{27,741,-38}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Feb 16 2025 *)

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

%K nonn,changed

%O 0,2

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