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A163287 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I. 1

%I

%S 1,49,2352,112896,5417832,259999488,12477267096,598778820864,

%T 28735144795560,1378987562102976,66177035471527512,

%U 3175808211876089664,152405705797427455464,7313885981134376257152,350990324575741067673624

%N Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

%C The initial terms coincide with those of A170768, 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="/A163287/b163287.txt">Table of n, a(n) for n = 0..590</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (47, 47, 47, -1128).

%F G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1128*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).

%F a(n) = 47*a(n-1)+47*a(n-2)+47*a(n-3)-1128*a(n-4). - _Wesley Ivan Hurt_, May 10 2021

%t CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(1128*t^4-47*t^3-47*t^2 - 47*t+1), {t,0,20}], t] (* or *) LinearRecurrence[{47, 47, 47, -1128}, {1,49,2352,112896,5417832}, 20] (* _G. C. Greubel_, Dec 17 2016 *)

%t coxG[{4, 1128, -47}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 01 2019 *)

%o (PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(1128*t^4-47*t^3 - 47*t^2-47*t+1)) \\ _G. C. Greubel_, Dec 17 2016

%o (MAGMA) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-48*x+1175*x^4-1128*x^5) )); // _G. C. Greubel_, May 01 2019

%o (Sage) ((1+x)*(1-x^4)/(1-48*x+1175*x^4-1128*x^5)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 01 2019

%o (GAP) a:=[49,2352,112896,5417832];; for n in [5..20] do a[n]:=47*(a[n-1]+a[n-2] +a[n-3] -24*a[n-4]); od; Concatenation([1], a); # _G. C. Greubel_, May 01 2019

%K nonn

%O 0,2

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

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Last modified July 25 10:05 EDT 2021. Contains 346289 sequences. (Running on oeis4.)