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A166170 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

%I A166170 #14 Mar 11 2020 19:05:08
%S A166170 1,38,1406,52022,1924814,71218118,2635070366,97497603542,
%T A166170 3607411331054,133474219248998,4938546112212223,182726206151826240,
%U A166170 6760869627616609176,250152176221778956464,9255630520204504816392
%N A166170 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C A166170 The initial terms coincide with those of A170757, although the two sequences are eventually different.
%C A166170 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166170 G. C. Greubel, <a href="/A166170/b166170.txt">Table of n, a(n) for n = 0..500</a>
%H A166170 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (36,36,36,36,36,36,36,36,36,-666).
%F A166170 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)/(666*t^10 - 36*t^9 - 36*t^8 - 36*t^7 - 36*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1).
%p A166170 seq(coeff(series((1+t)*(1-t^10)/(1-37*t+702*t^10-666*t^11), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Mar 11 2020
%t A166170 CoefficientList[Series[(1+t)*(1-t^10)/(1-37*t+702*t^10-666*t^11), {t,0,30}], t] (* _G. C. Greubel_, May 06 2016 *)
%t A166170 coxG[{666, 10, -36}] (* The coxG program is in A169452 *) (* _G. C. Greubel_, Mar 11 2020 *)
%o A166170 (Sage)
%o A166170 def A166170_list(prec):
%o A166170     P.<t> = PowerSeriesRing(ZZ, prec)
%o A166170     return P( (1+t)*(1-t^10)/(1-37*t+702*t^10-666*t^11) ).list()
%o A166170 A166170_list(30) # _G. C. Greubel_, Mar 11 2020
%K A166170 nonn
%O A166170 0,2
%A A166170 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009