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A163438 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%I A163438 #18 Jun 10 2025 20:51:55
%S A163438 1,13,156,1872,22464,269490,3232944,38784174,465276240,5581708704,
%T A163438 66961236342,803303685756,9636871221978,115609188148740,
%U A163438 1386911174446512,16638146470934274,199600322709006648
%N A163438 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163438 The initial terms coincide with those of A170732, although the two sequences are eventually different.
%C A163438 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163438 G. C. Greubel, <a href="/A163438/b163438.txt">Table of n, a(n) for n = 0..920</a>
%H A163438 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (11,11,11,11,-66).
%F A163438 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(66*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1).
%F A163438 a(n) = 11*a(n-1)+11*a(n-2)+11*a(n-3)+11*a(n-4)-66*a(n-5). - _Wesley Ivan Hurt_, May 10 2021
%t A163438 CoefficientList[Series[(1+x)*(1-x^5)/(1-12*x+77*x^5-66*x^6), {x, 0, 10}], x] (* or *) LinearRecurrence[{11, 11, 11, 11, -66}, {1, 13, 156, 1872, 22464, 269490}, 30] (* _G. C. Greubel_, Dec 23 2016 *)
%t A163438 coxG[{5, 66, -11}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 12 2019 *)
%o A163438 (PARI) my(x='x+O('x^30)); Vec((1+x)*(1-x^5)/(1-12*x+77*x^5-66*x^6)) \\ _G. C. Greubel_, Dec 23 2016
%o A163438 (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-12*x+77*x^5-66*x^6) )); // _G. C. Greubel_, May 12 2019
%o A163438 (Sage) ((1+x)*(1-x^5)/(1-12*x+77*x^5-66*x^6)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 12 2019
%K A163438 nonn,easy
%O A163438 0,2
%A A163438 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009