A166167 - OEIS

%I #14 Mar 11 2020 18:01:24

%S 1,37,1332,47952,1726272,62145792,2237248512,80540946432,

%T 2899474071552,104381066575872,3757718396730726,135277862282282160,

%U 4870003042161295290,175320109517775581520,6311523942638803173600

%N Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

%C The initial terms coincide with those of A170756, 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="/A166167/b166167.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 (35,35,35,35,35,35,35,35,35,-630).

%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)/(630*t^10 - 35*t^9 - 35*t^8 - 35*t^7 - 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 - 35*t^2 - 35*t + 1).

%p seq(coeff(series((1+t)*(1-t^10)/(1-36*t+665*t^10-630*t^11), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Mar 11 2020

%t CoefficientList[Series[(1+t)*(1-t^10)/(1-36*t+665*t^10-630*t^11), {t,0,30}], t] (* _G. C. Greubel_, May 06 2016 *)

%t coxG[{630, 10, -35}] (* The coxG program is in A169452 *) (* _G. C. Greubel_, Mar 11 2020 *)

%o (Sage)

%o def A166167_list(prec):

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

%o     return P( (1+t)*(1-t^10)/(1-36*t+665*t^10-630*t^11) ).list()

%o A166167_list(30) # _G. C. Greubel_, Mar 11 2020

%K nonn

%O 0,2

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