A166324 - OEIS

%I #20 Jun 08 2026 10:17:40

%S 1,49,2352,112896,5419008,260112384,12485394432,599298932736,

%T 28766348771328,1380784741023744,66277667569138536,

%U 3181328043318593280,152703746079289769112,7329779811805778917632,351829430966671148058624

%N Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

%C The initial terms coincide with those of A170768, 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="/A166324/b166324.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (47,47,47,47,47,47,47,47,47,-1128).

%F G.f.: (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)/(1128*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).

%p seq(coeff(series((1+t)*(1-t^10)/(1-48*t+1175*t^10-1128*t^11), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Mar 12 2020

%t CoefficientList[Series[(1+t)*(1-t^10)/(1-48*t+1175*t^10-1128*t^11), {t,0,30}], t] (* _G, C, Greubel_, May 09 2016 *)

%t coxG[{10, 1128, -47}] (* The coxG program is in A169452 *) (* _G. C. Greubel_, Mar 12 2020 *)

%o (SageMath)

%o def A166324_list(prec):

%o     P.<t> = PowerSeriesRing(ZZ, prec)

%o     return P( (1+t)*(1-t^10)/(1-48*t+1175*t^10-1128*t^11) ).list()

%o A166324_list(30) # _G. C. Greubel_, Mar 12 2020

%o (PARI) Vec((1+x^2+x^4+x^6+x^8)*(1+x)^2/(1-47*x-47*x^2-47*x^3-47*x^4-47*x^5-47*x^6-47*x^7-47*x^8-47*x^9+1128*x^10)+O(x^99)) \\ _Charles R Greathouse IV_, Jun 08 2026

%Y Cf. A170768, A154638.

%K nonn,easy

%O 0,2

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