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A166436 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%I A166436 #16 Jul 26 2024 06:01:25
%S A166436 1,42,1722,70602,2894682,118681962,4865960442,199504378122,
%T A166436 8179679503002,335366859623082,13750041244546362,563751691026399981,
%U A166436 23113819332082363920,947666592615375474240,38854330297230335138160
%N A166436 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166436 The initial terms coincide with those of A170761, although the two sequences are eventually different.
%C A166436 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166436 G. C. Greubel, <a href="/A166436/b166436.txt">Table of n, a(n) for n = 0..500</a>
%H A166436 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (40,40,40,40,40,40,40,40,40,40,-820).
%F A166436 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)/(820*t^11 - 40*t^10 - 40*t^9 - 40*t^8 - 40*t^7 - 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 - 40*t + 1).
%F A166436 From _G. C. Greubel_, Jul 26 2024: (Start)
%F A166436 a(n) = 40*Sum_{j=1..10} a(n-j) - 820*a(n-11).
%F A166436 G.f.: (1+x)*(1-x^11)/(1 - 41*x + 860*x^11 - 820*x^12). (End)
%t A166436 With[{p=820, q=40}, CoefficientList[Series[(1+t)*(1-t^11)/(1 - (q+1)*t + (p+q)*t^11 - p*t^12), {t,0,40}], t]] (* _G. C. Greubel_, May 14 2016; Jul 26 2024 *)
%t A166436 coxG[{11,820,-40}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 27 2024 *)
%o A166436 (Magma)
%o A166436 R<x>:=PowerSeriesRing(Integers(), 30);
%o A166436 Coefficients(R!( (1+x)*(1-x^11)/(1-41*x+860*x^11-820*x^12) )); // _G. C. Greubel_, Jul 26 2024
%o A166436 (SageMath)
%o A166436 def A166436_list(prec):
%o A166436     P.<x> = PowerSeriesRing(ZZ, prec)
%o A166436     return P( (1+x)*(1-x^11)/(1-41*x+860*x^11-820*x^12) ).list()
%o A166436 A166436_list(30) # _G. C. Greubel_, Jul 26 2024
%Y A166436 Cf. A154638, A169452, A170761.
%K A166436 nonn
%O A166436 0,2
%A A166436 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009