A166910 - OEIS

%I #12 Jul 05 2021 19:22:50

%S 1,8,56,392,2744,19208,134456,941192,6588344,46118408,322828856,

%T 2259801992,15818613944,110730297580,775112082864,5425784578704,

%U 37980492041520,265863444224784,1861044109112496,13027308760560528

%N Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.

%C The initial terms coincide with those of A003950, although the two sequences are eventually different.

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

%H G. C. Greubel, <a href="/A166910/b166910.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, -21).

%F G.f.: (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)/(21*t^13 - 6*t^12 - 6*t^11 - 6*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1).

%t CoefficientList[Series[(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)/(21*t^13 - 6*t^12 - 6*t^11 - 6*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, May 28 2016 *)

%t coxG[{13,21,-6}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 05 2021 *)

%K nonn

%O 0,2

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