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%I #19 Sep 08 2022 08:45:48
%S 1,15,210,2940,41160,576240,8067360,112943040,1581202560,22136835840,
%T 309915701655,4338819821700,60743477483325,850408684479900,
%U 11905721578705500,166680102045693600,2333521427853142800
%N Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C The initial terms coincide with those of A170734, 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="/A165875/b165875.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 (13,13,13,13,13,13,13,13,13,-91).
%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)/(91*t^10 - 13*t^9 - 13*t^8 - 13*t^7 - 13*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1).
%p seq(coeff(series((1+t)*(1-t^10)/(1-14*t+104*t^10-91*t^11), t, n+1), t, n), n = 0..20); # _G. C. Greubel_, Sep 23 2019
%t CoefficientList[Series[(1+t)*(1-t^10)/(1-14*t+104*t^10-91*t^11), {t, 0, 25}], t] (* _G. C. Greubel_, Apr 17 2016 *)
%t coxG[{10, 91, -13}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Sep 23 2019 *)
%o (PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-14*t+104*t^10-91*t^11)) \\ _G. C. Greubel_, Sep 23 2019
%o (Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-14*t+104*t^10-91*t^11) )); // _G. C. Greubel_, Sep 23 2019
%o (Sage)
%o def A165875_list(prec):
%o P.<t> = PowerSeriesRing(ZZ, prec)
%o return P((1+t)*(1-t^10)/(1-14*t+104*t^10-91*t^11)).list()
%o A165875_list(30) # _G. C. Greubel_, Sep 23 2019
%o (GAP) a:=[15, 210, 2940, 41160, 576240, 8067360, 112943040, 1581202560, 22136835840, 309915701655];; for n in [11..20] do a[n]:=13*Sum([1..9], j-> a[n-j]) -19*a[n-10]; od; Concatenation([1], a); # _G. C. Greubel_, Sep 23 2019
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
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