Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #14 Sep 08 2022 08:45:48
%S 1,10,90,810,7290,65610,590490,5314410,47829690,430467210,3874204845,
%T 34867843200,313810585200,2824295234400,25418656818000,
%U 228767908737600,2058911155018800,18530200182592800,166771799730147600
%N Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C The initial terms coincide with those of A003952, although the two sequences are eventually different.
%C Computed with MAGMA using commands similar to those used to compute A154638.
%H G. C. Greubel, <a href="/A165788/b165788.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (8,8,8,8,8,8,8,8,8,-36).
%F 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)/(36*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).
%p seq(coeff(series((1+t)*(1-t^10)/(1-9*t+44*t^10-36*t^11), t, n+1), t, n), n = 0..20); # _G. C. Greubel_, Aug 10 2019
%t CoefficientList[Series[(1+t)*(1-t^10)/(1-9*t+44*t^10-36*t^11), {t, 0, 25}], t] (* _G. C. Greubel_, Apr 08 2016 *)
%t coxG[{10, 36, -8}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Sep 22 2019 *)
%o (PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-9*t+44*t^10-36*t^11)) \\ _G. C. Greubel_, Sep 22 2019
%o (Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-9*t+44*t^10-36*t^11) )); // _G. C. Greubel_, Sep 22 2019
%o (Sage)
%o def A165788_list(prec):
%o P.<t> = PowerSeriesRing(ZZ, prec)
%o return P((1+t)*(1-t^10)/(1-9*t+44*t^10-36*t^11)).list()
%o A165788_list(20) # _G. C. Greubel_, Sep 22 2019
%o (GAP) a:=[10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204845];; for n in [11..20] do a[n]:=8*Sum([1..9], j-> a[n-j]) -36*a[n-10]; od; Concatenation([1], a); # _G. C. Greubel_, Sep 22 2019
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009