A166303 - OEIS

%I #14 Mar 11 2020 18:43:20

%S 1,46,2070,93150,4191750,188628750,8488293750,381973218750,

%T 17188794843750,773495767968750,34807309558592715,1566328930136625600,

%U 70484801856146057160,3171816083526478304400,142731723758687281647000

%N Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

%C The initial terms coincide with those of A170765, 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="/A166303/b166303.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 (44, 44, 44, 44, 44, 44, 44, 44, 44, -990).

%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)/(990*t^10 - 44*t^9 - 44*t^8 - 44*t^7 - 44*t^6 - 44*t^5 - 44*t^4 - 44*t^3 - 44*t^2 - 44*t + 1).

%p seq(coeff(series((1+t)*(1-t^10)/(1-45*t+1034*t^10-990*t^11), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Mar 11 2020

%t CoefficientList[Series[(1+t)*(1-t^10)/(1-45*t+1034*t^10-990*t^11), {t,0,30}], t] (* _G. C. Greubel_, May 09 2016 *)

%t coxG[{10, 990, -44}] (* The coxG program is in A169452 *) (* _G. C. Greubel_, Mar 11 2020 *)

%o (Sage)

%o def A166303_list(prec):

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

%o     return P((1+t)*(1-t^10)/(1-45*t+1034*t^10-990*t^11)).list()

%o A166303_list(30) # _G. C. Greubel_, Mar 11 2020

%K nonn

%O 0,2

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