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A166377 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.

%I A166377 #16 Sep 08 2022 08:45:48
%S A166377 1,13,156,1872,22464,269568,3234816,38817792,465813504,5589762048,
%T A166377 67077144576,804925734834,9659108817072,115909305793710,
%U A166377 1390911669390672,16690940031081888,200291280353708544
%N A166377 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 A166377 The initial terms coincide with those of A170732, although the two sequences are eventually different.
%C A166377 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166377 G. C. Greubel, <a href="/A166377/b166377.txt">Table of n, a(n) for n = 0..500</a>
%H A166377 <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 A166377 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 A166377 G.f.: (1 + t - t^11 - t^12)/(1 - 12*t + 77*t^11 - 66*t^12). - _Zak Seidov_, Dec 05 2009
%t A166377 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 A166377 (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 A166377 (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 A166377 (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 A166377 nonn
%O A166377 0,2
%A A166377 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009