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A163266 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I. 1

%I

%S 1,48,2256,106032,4982376,234118656,11001086208,516933992448,

%T 24290397127896,1141390199234256,53633194222120752,

%U 2520189436004377296,118422087020288430408,5564578001118314478240,261475955285477822620512

%N Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

%C The initial terms coincide with those of A170767, 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="/A163266/b163266.txt">Table of n, a(n) for n = 0..595</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (46, 46, 46, -1081).

%F G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1081*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).

%t CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(1081*t^4-46*t^3-46*t^2 - 46*t+1), {t,0,20}], t] (* or *) Join[{1}, LinearRecurrence[ {46,46,46,-1081}, {48,2256,106032,4982376}, 20] (* _G. C. Greubel_, Dec 12 2016 *)

%t coxG[{4, 1081, -46}] (* 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)/(1081*t^4-46*t^3 - 46*t^2-46*t+1)) \\ _G. C. Greubel_, Dec 12 2016 *)

%o (MAGMA) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-47*x+1127*x^4-1081*x^5) )); // _G. C. Greubel_, May 01 2019

%o (Sage) ((1+x)*(1-x^4)/(1-47*x+1127*x^4-1081*x^5)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 01 2019

%o (GAP) a:=[48,2256,106032,4982376];; for n in [5..20] do a[n]:=46*(a[n-1] +a[n-2] +a[n-3]) -1081*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 November 13 07:13 EST 2019. Contains 329085 sequences. (Running on oeis4.)