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%I A165796 #18 Sep 08 2022 08:45:48
%S A165796 1,11,110,1100,11000,110000,1100000,11000000,110000000,1100000000,
%T A165796 10999999945,109999998900,1099999983555,10999999781100,
%U A165796 109999997266500,1099999967220000,10999999617750000,109999995633000000
%N A165796 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C A165796 The initial terms coincide with those of A003953, although the two sequences are eventually different.
%C A165796 Computed with MAGMA using commands similar to those used to compute A154638.
%C A165796 a(0) = a(1) = 1 (mod 5), a(n) = 0 (mod 5) for n>=2. - _G. C. Greubel_, Apr 08 2016
%H A165796 G. C. Greubel, <a href="/A165796/b165796.txt">Table of n, a(n) for n = 0..500</a>
%H A165796 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (9,9,9,9,9,9,9,9,9,-45).
%F A165796 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)/(45*t^10 - 9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).
%p A165796 seq(coeff(series((1+t)*(1-t^10)/(1-10*t+54*t^10-45*t^11), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Sep 22 2019
%t A165796 CoefficientList[Series[(1+t)*(1-t^10)/(1-10*t+54*t^10-45*t^11), {t, 0, 25}], t] (* _G. C. Greubel_, Apr 08 2016 *)
%t A165796 coxG[{10, 45, -9}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Sep 22 2019 *)
%o A165796 (PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-10*t+54*t^10-45*t^11)) \\ _G. C. Greubel_, Sep 22 2019
%o A165796 (Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-10*t+54*t^10-45*t^11) )); // _G. C. Greubel_, Sep 22 2019
%o A165796 (Sage)
%o A165796 def A165796_list(prec):
%o A165796     P.<t> = PowerSeriesRing(ZZ, prec)
%o A165796     return P((1+t)*(1-t^10)/(1-10*t+54*t^10-45*t^11)).list()
%o A165796 A165796_list(20) # _G. C. Greubel_, Sep 22 2019
%o A165796 (GAP) a:=[11, 110, 1100, 11000, 110000, 1100000, 11000000, 110000000, 1100000000, 10999999945];; for n in [11..20] do a[n]:=9*Sum([1..9], j-> a[n-j]) -45*a[n-10]; od; Concatenation([1], a); # _G. C. Greubel_, Sep 22 2019
%K A165796 nonn
%O A165796 0,2
%A A165796 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009

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