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A166167 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.

%I A166167 #14 Mar 11 2020 18:01:24
%S A166167 1,37,1332,47952,1726272,62145792,2237248512,80540946432,
%T A166167 2899474071552,104381066575872,3757718396730726,135277862282282160,
%U A166167 4870003042161295290,175320109517775581520,6311523942638803173600
%N A166167 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 A166167 The initial terms coincide with those of A170756, although the two sequences are eventually different.
%C A166167 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166167 G. C. Greubel, <a href="/A166167/b166167.txt">Table of n, a(n) for n = 0..500</a>
%H A166167 <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 A166167 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 A166167 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 A166167 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 A166167 coxG[{630, 10, -35}] (* The coxG program is in A169452 *) (* _G. C. Greubel_, Mar 11 2020 *)
%o A166167 (Sage)
%o A166167 def A166167_list(prec):
%o A166167     P.<t> = PowerSeriesRing(ZZ, prec)
%o A166167     return P( (1+t)*(1-t^10)/(1-36*t+665*t^10-630*t^11) ).list()
%o A166167 A166167_list(30) # _G. C. Greubel_, Mar 11 2020
%K A166167 nonn
%O A166167 0,2
%A A166167 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009