A166026 - OEIS

%I #16 Sep 08 2022 08:45:48

%S 1,30,870,25230,731670,21218430,615334470,17844699630,517496289270,

%T 15007392388830,435214379275635,12621216998980800,366015292970077800,

%U 10614443496121659600,307818861387220827000,8926746980220492242400

%N Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

%C The initial terms coincide with those of A170749, 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="/A166026/b166026.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 (28,28,28,28,28,28,28,28,28,-406).

%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)/(406*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).

%p seq(coeff(series((1+t)*(1-t^10)/(1-29*t+334*t^10-406*t^11), t, n+1), t, n), n = 0..30); # _G. C. Greubel_, Dec 05 2019

%t CoefficientList[Series[(1+t)*(1-t^10)/(1-29*t+334*t^10-406*t^11), {t,0,30}], t] (* _G. C. Greubel_, Apr 21 2016 *)

%t coxG[{10,406,-28}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 13 2020 *)

%o (PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-29*t+334*t^10-406*t^11)) \\ _G. C. Greubel_, Dec 05 2019

%o (Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-29*t+334*t^10-406*t^11) )); // _G. C. Greubel_, Dec 05 2019

%o (Sage)

%o def A166026_list(prec):

%o     P.<t> = PowerSeriesRing(ZZ, prec)

%o     return P((1+t)*(1-t^10)/(1-29*t+334*t^10-406*t^11)).list()

%o A166026_list(30) # _G. C. Greubel_, Dec 05 2019

%o (GAP) a:=[30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379275635];; for n in [11..30] do a[n]:=28*Sum([1..9], j-> a[n-j]) - 406*a[n-10]; od; Concatenation([1], a); # _G. C. Greubel_, Dec 05 2019

%K nonn

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009