A163552 - OEIS

%I #26 Sep 08 2022 08:45:46

%S 1,30,870,25230,731670,21217995,615309240,17843602560,517453877640,

%T 15005855150160,435160887802830,12619407316577880,365955317872798920,

%U 10612486887830912280,307755817292235608520,8924735934026717183820

%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)^5 = 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 Vincenzo Librandi, <a href="/A163552/b163552.txt">Table of n, a(n) for n = 0..696</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (28, 28, 28, 28, -406).

%F G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(406*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).

%F a(n) = 28*a(n-1)+28*a(n-2)+28*a(n-3)+28*a(n-4)-406*a(n-5). - _Wesley Ivan Hurt_, May 11 2021

%t CoefficientList[Series[(x^5+2*x^4+2*x^3+2*x^2+2*x+1)/(406*x^5-28*x^4 - 28*x^3-28*x^2-28*x+1), {x, 0, 20}], x] (* _Wesley Ivan Hurt_, Mar 31 2017 *)

%t LinearRecurrence[{28,28,28,28,-406}, {1,30,870,25230,731670,21217995}, 20] (* _Vincenzo Librandi_, Apr 01 2017 *)

%t coxG[{5, 406, -28}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 16 2019 *)

%o (Magma) I:=[1,30,870,25230,731670,21217995]; [n le 6 select I[n] else 28*Self(n-1)+28*Self(n-2)+28*Self(n-3)+28*Self(n-4)-406*Self(n-5): n in [1..30]]; // _Vincenzo Librandi_, Apr 01 2017

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-29*x+434*x^5-406*x^6) )); // _G. C. Greubel_, May 16 2019

%o (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-29*x+434*x^5-406*x^6)) \\ _G. C. Greubel_, Jul 28 2017

%o (Sage) ((1+x)*(1-x^5)/(1-29*x+434*x^5-406*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 16 2019

%K nonn

%O 0,2

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