cp's OEIS Frontend

A163453 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%I A163453 #19 Jun 10 2025 20:53:10
%S A163453 1,19,342,6156,110808,1994373,35895636,646066215,11628197676,
%T A163453 209289662676,3766891838382,67798255971825,1220264268268608,
%U A163453 21962878883360919,395298019772086050,7114756005603413388
%N A163453 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163453 The initial terms coincide with those of A170738, although the two sequences are eventually different.
%C A163453 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163453 G. C. Greubel, <a href="/A163453/b163453.txt">Table of n, a(n) for n = 0..790</a>
%H A163453 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (17,17,17,17,-153).
%F A163453 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(153*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1).
%F A163453 a(n) = 17*a(n-1)+17*a(n-2)+17*a(n-3)+17*a(n-4)-153*a(n-5). - _Wesley Ivan Hurt_, May 10 2021
%t A163453 CoefficientList[Series[(1+x)*(1-x^5)/(1-18*x+170*x^5-153*x^6), {x, 0, 20}], x] (* or *) LinearRecurrence[{17, 17, 17, 17, -153}, {1, 19, 342, 6156, 110808, 1994373}, 20] (* _G. C. Greubel_, Dec 24 2016 *)
%t A163453 coxG[{5, 153, -17}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 13 2019 *)
%o A163453 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-18*x+170*x^5-153*x^6)) \\ _G. C. Greubel_, Dec 24 2016
%o A163453 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-18*x+170*x^5-153*x^6) )); // _G. C. Greubel_, May 13 2019
%o A163453 (Sage) ((1+x)*(1-x^5)/(1-18*x+170*x^5-153*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 13 2019
%K A163453 nonn,easy
%O A163453 0,2
%A A163453 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009