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A166379 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%I A166379 #22 Sep 08 2022 08:45:48
%S A166379 1,14,182,2366,30758,399854,5198102,67575326,878479238,11420230094,
%T A166379 148462991222,1930018885795,25090245514152,326173191668688,
%U A166379 4240251491494200,55123269386840928,716602501995344328
%N A166379 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166379 The initial terms coincide with those of A170733, although the two sequences are eventually different.
%C A166379 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166379 G. C. Greubel, <a href="/A166379/b166379.txt">Table of n, a(n) for n = 0..500</a>
%H A166379 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (12, 12, 12, 12, 12, 12, 12, 12, 12, 12, -78).
%F A166379 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)/(78*t^11 - 12*t^10 - 12*t^9 - 12*t^8 - 12*t^7 - 12*t^6 - 12*t^5 - 12*t^4 - 12*t^3 - 12*t^2 - 12*t + 1).
%F A166379 G.f.: (1+x)*(1-x^11)/(1 -13*x +90*x^11 -78*x^12). - _G. C. Greubel_, Apr 26 2019
%F A166379 a(n) = -78*a(n-11) + 12*Sum_{k=1..10} a(n-k). - _Wesley Ivan Hurt_, May 06 2021
%t A166379 CoefficientList[Series[(1+x)*(1-x^11)/(1 -13*x +90*x^11 -78*x^12), {x, 0, 20}], x] (* _G. C. Greubel_, May 10 2016, modified Apr 26 2019 *)
%t A166379 coxG[{11,78,-12}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Nov 30 2016 *)
%o A166379 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^11)/(1-13*x+90*x^11-78*x^12)) \\ _G. C. Greubel_, Apr 26 2019
%o A166379 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^11)/(1-13*x+90*x^11-78*x^12) )); // _G. C. Greubel_, Apr 26 2019
%o A166379 (Sage) ((1+x)*(1-x^11)/(1-13*x+90*x^11-78*x^12)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 26 2019
%K A166379 nonn,easy
%O A166379 0,2
%A A166379 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009