cp's OEIS Frontend

A163265 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

%I A163265 #18 Jun 10 2025 20:40:25
%S A163265 1,47,2162,99452,4573711,210340980,9673398765,444871172700,
%T A163265 20459237269140,940902479912925,43271284508242650,1990008638480367675,
%U A163265 91518761835509986350,4208868045065726973000,193562170919821248573375
%N A163265 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
%C A163265 The initial terms coincide with those of A170766, although the two sequences are eventually different.
%C A163265 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163265 G. C. Greubel, <a href="/A163265/b163265.txt">Table of n, a(n) for n = 0..600</a>
%H A163265 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (45, 45, 45, -1035).
%F A163265 G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1035*t^4 - 45*t^3 - 45*t^2 - 45*t + 1).
%F A163265 a(n) = 45*a(n-1)+45*a(n-2)+45*a(n-3)-1035*a(n-4). - _Wesley Ivan Hurt_, May 10 2021
%t A163265 CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(1035*t^4-45*t^3-45*t^2 - 45*t+1), {t,0,20}], t] (* or *) LinearRecurrence[ {45, 45, 45, -1035}, {1,47,2162,99452,4573711}, 20] (* _G. C. Greubel_, Dec 12 2016 *)
%t A163265 coxG[{4, 1035, -45}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 01 2019 *)
%o A163265 (PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(1035*t^4-45*t^3- 45*t^2-45*t+1)) \\ _G. C. Greubel_, Dec 12 2016
%o A163265 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-46*x+1080*x^4-1035*x^5) )); // _G. C. Greubel_, May 01 2019
%o A163265 (Sage) ((1+x)*(1-x^4)/(1-46*x+1080*x^4-1035*x^5)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 01 2019
%o A163265 (GAP) a:=[47,2162,99452,4573711];; for n in [5..20] do a[n]:=45*(a[n-1]+a[n-2] +a[n-3]-23*a[n-4]); od; Concatenation([1], a); # _G. C. Greubel_, May 01 2019
%K A163265 nonn,easy
%O A163265 0,2
%A A163265 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009