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A166437 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%I A166437 #16 Jul 26 2024 05:59:46
%S A166437 1,43,1806,75852,3185784,133802928,5619722976,236028364992,
%T A166437 9913191329664,416354035845888,17486869505527296,734448519232145529,
%U A166437 30846837807750074292,1295567187925501528275,54413821892870997324012
%N A166437 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166437 The initial terms coincide with those of A170762, although the two sequences are eventually different.
%C A166437 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166437 G. C. Greubel, <a href="/A166437/b166437.txt">Table of n, a(n) for n = 0..500</a>
%H A166437 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (41,41,41,41,41,41,41,41,41,41,-861).
%F A166437 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)/(861*t^11 - 41*t^10 - 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).
%F A166437 a(n) = -861*a(n-11) + 41*Sum_{k=1..10} a(n-k). - _Wesley Ivan Hurt_, Mar 17 2023
%F A166437 G.f.: (1+x)*(1-x^11)/(1 - 42*x + 902*x^11 - 861*x^12). - _G. C. Greubel_, Jul 26 2024
%t A166437 With[{p=861, q=41}, 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 A166437 coxG[{11, 861, -41, 30}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Jul 26 2024 *)
%o A166437 (Magma)
%o A166437 R<x>:=PowerSeriesRing(Integers(), 30);
%o A166437 f:= func< p,q,x | (1+x)*(1-x^11)/(1-(q+1)*x+(p+q)*x^11-p*x^12) >;
%o A166437 Coefficients(R!( f(861,41,x) )); // _G. C. Greubel_, Jul 26 2024
%o A166437 (SageMath)
%o A166437 def f(p,q,x): return (1+x)*(1-x^11)/(1-(q+1)*x+(p+q)*x^11-p*x^12)
%o A166437 def A166437_list(prec):
%o A166437     P.<x> = PowerSeriesRing(ZZ, prec)
%o A166437     return P( f(861,41,x) ).list()
%o A166437 A166437_list(30) # _G. C. Greubel_, Jul 26 2024
%Y A166437 Cf. A154638, A169452, A170762.
%K A166437 nonn
%O A166437 0,2
%A A166437 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009