A167087 - OEIS

%I #13 Mar 01 2022 12:38:21

%S 1,34,1122,37026,1221858,40321314,1330603362,43909910946,

%T 1449027061218,47817893020194,1577990469666402,52073685498991266,

%U 1718431621466711778,56708243508401488113,1871372035777249089216,61755277180649219333760

%N Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.

%C The initial terms coincide with those of A170753, 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="/A167087/b167087.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 (32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, -528).

%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)/(528*t^13 - 32*t^12 - 32*t^11 - 32*t^10 - 32*t^9 - 32*t^8 - 32*t^7 - 32*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*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)/(528*t^13 - 32*t^12 - 32*t^11 - 32*t^10 - 32*t^9 - 32*t^8 - 32*t^7 - 32*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1), {t, 0, 20}], t] (* _G. C. Greubel_, Jun 01 2016 *)

%t coxG[{13,528,-32}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Mar 01 2022 *)

%Y Cf. A154638, A170753.

%K nonn

%O 0,2

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