A166313 - OEIS

%I #22 Jun 08 2026 10:17:30

%S 1,48,2256,106032,4983504,234224688,11008560336,517402335792,

%T 24317909782224,1142941759764528,53718262708931688,

%U 2524758347319736320,118663642324025116416,5577191189229063412224,262127985893760478586112

%N Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

%C The initial terms coincide with those of A170767, 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="/A166313/b166313.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 (46,46,46,46,46,46,46,46,46,-1081).

%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)/(1081*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).

%p seq(coeff(series((1+t)*(1-t^10)/(1-47*t+1127*t^10-1081*t^11), t, n+1), t, n), n = 0..30); # _G. C. Greubel_, Mar 11 2020

%t CoefficientList[Series[(1+t)*(1-t^10)/(1-47*t+1127*t^10-1081*t^11), {t,0,30}], t] (* _G. C. Greubel_, May 09 2016 *)

%t coxG[{10,1081,-46}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 05 2017 *)

%o (SageMath)

%o def A166313_list(prec):

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

%o     return P( (1+t)*(1-t^10)/(1-47*t+1127*t^10-1081*t^11) ).list()

%o A166313_list(30) # _G. C. Greubel_, Mar 11 2020

%o (PARI) Vec((1+x^2+x^4+x^6+x^8)*(1+x)^2/(1-46*x-46*x^2-46*x^3-46*x^4-46*x^5-46*x^6-46*x^7-46*x^8-46*x^9+1081*x^10)+O(x^99)) \\ _Charles R Greathouse IV_, Jun 08 2026

%Y Cf. A170767, A154638.

%K nonn,easy

%O 0,2

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