A165703 - OEIS

A165703

Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

%I #8 Nov 23 2016 22:18:51

%S 1,47,2162,99452,4574792,210440432,9680259872,445291954112,

%T 20483429889152,942237774899911,43342937645346180,1993775131683637965,

%U 91713656057342175900,4218828178632902248860,194066096216890962690720

%N Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

%C The initial terms coincide with those of A170766, although the two sequences are eventually different.

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

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (45, 45, 45, 45, 45, 45, 45, 45, -1035).

%F G.f. (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 +

%F 1)/(1035*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 -

%F 45*t^2 - 45*t + 1)

%t coxG[{9,1035,-45}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Feb 25 2015 *)

%K nonn

%O 0,2

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