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A163552 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.

%I A163552 #26 Sep 08 2022 08:45:46
%S A163552 1,30,870,25230,731670,21217995,615309240,17843602560,517453877640,
%T A163552 15005855150160,435160887802830,12619407316577880,365955317872798920,
%U A163552 10612486887830912280,307755817292235608520,8924735934026717183820
%N A163552 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 A163552 The initial terms coincide with those of A170749, although the two sequences are eventually different.
%C A163552 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163552 Vincenzo Librandi, <a href="/A163552/b163552.txt">Table of n, a(n) for n = 0..696</a>
%H A163552 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (28, 28, 28, 28, -406).
%F A163552 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 A163552 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 A163552 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 A163552 LinearRecurrence[{28,28,28,28,-406}, {1,30,870,25230,731670,21217995}, 20] (* _Vincenzo Librandi_, Apr 01 2017 *)
%t A163552 coxG[{5, 406, -28}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 16 2019 *)
%o A163552 (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 A163552 (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 A163552 (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 A163552 (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 A163552 nonn
%O A163552 0,2
%A A163552 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009