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A166233 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

%I A166233 #16 Mar 11 2020 21:26:36
%S A166233 1,43,1806,75852,3185784,133802928,5619722976,236028364992,
%T A166233 9913191329664,416354035845888,17486869505526393,734448519232070580,
%U A166233 30846837807745372371,1295567187925238776044,54413821892857220325252
%N A166233 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C A166233 The initial terms coincide with those of A170762, although the two sequences are eventually different.
%C A166233 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166233 G. C. Greubel, <a href="/A166233/b166233.txt">Table of n, a(n) for n = 0..500</a>
%H A166233 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (41, 41, 41, 41, 41, 41, 41, 41, 41, -861).
%F A166233 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)/(861*t^10 - 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).
%p A166233 seq(coeff(series((1+t)*(1-t^10)/(1-42*t+902*t^10-861*t^11), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Mar 11 2020
%t A166233 CoefficientList[Series[(1+t)*(1-t^10)/(1-42*t+902*t^10-861*t^11), {t,0,30}], t] (* _G. C. Greubel_, May 07 2016 *)
%t A166233 coxG[{10,861,-41}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 10 2018 *)
%o A166233 (Sage)
%o A166233 def A166233_list(prec):
%o A166233     P.<t> = PowerSeriesRing(ZZ, prec)
%o A166233     return P( (1+t)*(1-t^10)/(1-42*t+902*t^10-861*t^11) ).list()
%o A166233 A166233_list(30) # _G. C. Greubel_, Aug 10 2019
%K A166233 nonn
%O A166233 0,2
%A A166233 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009