%I #16 Sep 08 2022 08:45:48

%S 1,13,156,1872,22464,269568,3234816,38817792,465813504,5589762048,

%T 67077144576,804925734834,9659108817072,115909305793710,

%U 1390911669390672,16690940031081888,200291280353708544

%N Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%C The initial terms coincide with those of A170732, although the two sequences are eventually different.

%C Computed with MAGMA using commands similar to those used to compute A154638.

%H G. C. Greubel, <a href="/A166377/b166377.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11, 11, 11, 11, 11, 11, 11, 11, 11, 11, -66).

%F G.f.: (t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(66*t^11 - 11*t^10 - 11*t^9 - 11*t^8 - 11*t^7 - 11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1).

%F G.f.: (1 + t - t^11 - t^12)/(1 - 12*t + 77*t^11 - 66*t^12). - _Zak Seidov_, Dec 05 2009

%t CoefficientList[Series[(1+t)*(1-t^11)/(1-12*t+77*t^11-66*t^12), {t, 0, 20}], t] (* _G. C. Greubel_, May 10 2016 *)

%o (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^11)/(1-12*x+77*x^11-66*x^12)) \\ _G. C. Greubel_, Apr 25 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^11)/(1-12*x+77*x^11-66*x^12) )); // _G. C. Greubel_, Apr 25 2019

%o (Sage) ((1+x)*(1-x^11)/(1-12*x+77*x^11-66*x^12)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 25 2019

%K nonn

%O 0,2

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