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A165456 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I. 1

%I

%S 1,28,756,20412,551124,14880348,401769396,10847773692,292889889684,

%T 7908027021090,213516729559224,5764951697823864,155653695833814360,

%U 4202649787312378584,113471544252017775096,3063731694658235867448

%N Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

%C The initial terms coincide with those of A170747, 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="/A165456/b165456.txt">Table of n, a(n) for n = 0..695</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (26,26,26,26,26,26,26,26,-351).

%F G.f.: (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)/(351*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 -26*t^2 - 26*t + 1).

%p seq(coeff(series((x^9+2*x^8+2*x^7+2*x^6+2*x^5+2*x^4+2*x^3+2*x^2+2*x+1)/( 351*x^9-26*x^8-26*x^7-26*x^6-26*x^5-26*x^4-26*x^3-26*x^2-26*x+1),x, n+1), x, n), n = 0 .. 15); # _Muniru A Asiru_, Oct 21 2018

%t CoefficientList[Series[(1+t)*(1-t^9)/(1-27*t+377*t^9-351*t^10), {t, 0, 30}], t] (* _G. C. Greubel_, Oct 20 2018 *)

%t coxG[{9, 351, -26}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Sep 16 2019 *)

%o (PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^9)/(1-27*t+377*t^9-351*t^10)) \\ _G. C. Greubel_, Oct 20 2018

%o (MAGMA) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^9)/(1-27*t+377*t^9-351*t^10) )); // _G. C. Greubel_, Oct 20 2018

%o (Sage)

%o def A165456_list(prec):

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

%o return P((1+t)*(1-t^9)/(1-27*t+377*t^9-351*t^10)).list()

%o A165456_list(20) # _G. C. Greubel_, Sep 16 2019

%o (GAP) a:=[28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021090];; for n in [10..20] do a[n]:=326*Sum([1..8], j-> a[n-j]) -351*a[n-9]; od; Concatenation([1], a); # _G. C. Greubel_, Sep 16 2019

%K nonn,easy

%O 0,2

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

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Last modified July 24 08:43 EDT 2021. Contains 346273 sequences. (Running on oeis4.)