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A166165 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

%I A166165 #12 Mar 11 2020 17:11:45
%S A166165 1,36,1260,44100,1543500,54022500,1890787500,66177562500,
%T A166165 2316214687500,81067514062500,2837362992186870,99307704726518400,
%U A166165 3475769665427372880,121651938289931061600,4257817840146642534000,149023624405099426920000
%N A166165 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C A166165 The initial terms coincide with those of A170755, although the two sequences are eventually different.
%C A166165 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166165 G. C. Greubel, <a href="/A166165/b166165.txt">Table of n, a(n) for n = 0..500</a>
%H A166165 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (34, 34, 34, 34, 34, 34, 34, 34, 34, -595).
%F A166165 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)/(595*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).
%p A166165 seq(coeff(series((1+t)*(1-t^10)/(1-35*t+629*t^10-595*t^11), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Mar 11 2020
%t A166165 CoefficientList[Series[(1+t)*(1-t^10)/(1-35*t+629*t^10-595*t^11), {t,0,30}], t] (* _G. C. Greubel_, May 06 2016 *)
%t A166165 coxG[{595, 10, -34}] (* The coxG program is in A169452 *) (* _G. C. Greubel_, Mar 11 2020 *)
%o A166165 (Sage)
%o A166165 def A166165_list(prec):
%o A166165     P.<t> = PowerSeriesRing(ZZ, prec)
%o A166165     return P( (1+t)*(1-t^10)/(1-35*t+629*t^10-595*t^11) ).list()
%o A166165 A166165_list(30) # _G. C. Greubel_, Mar 11 2020
%K A166165 nonn
%O A166165 0,2
%A A166165 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009