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A166145 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

%I A166145 #17 Mar 11 2020 17:13:28
%S A166145 1,35,1190,40460,1375640,46771760,1590239840,54068154560,
%T A166145 1838317255040,62502786671360,2125094746825645,72253221392051700,
%U A166145 2456609527329070575,83524723929165033900,2839840613590816720500,96554580862060757805600
%N A166145 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C A166145 The initial terms coincide with those of A170754, although the two sequences are eventually different.
%C A166145 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166145 G. C. Greubel, <a href="/A166145/b166145.txt">Table of n, a(n) for n = 0..500</a>
%H A166145 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (33, 33, 33, 33, 33, 33, 33, 33, 33, -561).
%F A166145 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)/(561*t^10 - 33*t^9 - 33*t^8 - 33*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).
%p A166145 seq(coeff(series((1+t)*(1-t^10)/(1-34*t+594*t^10-561*t^11), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Mar 11 2020
%t A166145 CoefficientList[Series[(1+t)*(1-t^10)/(1-34*t+594*t^10-561*t^11), {t, 0, 30}], t] (* _G. C. Greubel_, Apr 27 2016 *)
%t A166145 coxG[{561, 10, -33}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Mar 11 2020 *)
%o A166145 (Sage)
%o A166145 def A166145_list(prec):
%o A166145     P.<t> = PowerSeriesRing(ZZ, prec)
%o A166145     return P( (1+t)*(1-t^10)/(1-34*t+594*t^10-561*t^11) ).list()
%o A166145 A166145_list(30) # _G. C. Greubel_, Mar 11 2020
%K A166145 nonn
%O A166145 0,2
%A A166145 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009