A169307 - OEIS

%I #10 May 10 2018 01:36:35

%S 1,6,30,150,750,3750,18750,93750,468750,2343750,11718750,58593750,

%T 292968750,1464843750,7324218750,36621093750,183105468750,

%U 915527343750,4577636718750,22888183593750,114440917968750,572204589843750

%N Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.

%C The initial terms coincide with those of A003948, although the two sequences are eventually different.

%C First disagreement at index 30: a(30) = 1117587089538574218735, A003948(30) = 1117587089538574218750. - _Klaus Brockhaus_, Jun 22 2011

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

%H <a href="/index/Rec#order_30">Index entries for linear recurrences with constant coefficients</a>, signature (4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -10).

%F G.f.: (t^30 + 2*t^29 + 2*t^28 + 2*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)/(10*t^30 - 4*t^29 - 4*t^28 - 4*t^27 - 4*t^26 - 4*t^25 - 4*t^24 - 4*t^23 - 4*t^22 - 4*t^21 - 4*t^20 - 4*t^19 - 4*t^18 - 4*t^17 - 4*t^16 - 4*t^15 - 4*t^14 - 4*t^13 - 4*t^12 - 4*t^11 - 4*t^10 - 4*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t + 1).

%Y Cf. A003948 (G.f.: (1+x)/(1-5*x)).

%K nonn

%O 0,2

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