cp's OEIS Frontend

A166438 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%I A166438 #17 Jul 26 2024 05:59:21
%S A166438 1,44,1892,81356,3498308,150427244,6468371492,278139974156,
%T A166438 11960018888708,514280812214444,22114074925221092,950905221784506010,
%U A166438 40888924536733717752,1758223755079548115128,75603621468420493777560
%N A166438 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166438 The initial terms coincide with those of A170763, although the two sequences are eventually different.
%C A166438 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166438 G. C. Greubel, <a href="/A166438/b166438.txt">Table of n, a(n) for n = 0..500</a>
%H A166438 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (42,42,42,42,42,42,42,42,42,42,-903).
%F A166438 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)/(903*t^11 - 42*t^10 - 42*t^9 - 42*t^8 - 42*t^7 - 42*t^6 - 42*t^5 - 42*t^4 - 42*t^3 - 42*t^2 - 42*t + 1).
%F A166438 From _G. C. Greubel_, Jul 26 2024: (Start)
%F A166438 a(n) = 42*Sum_{j=1..10} a(n-j) - 903*a(n-11).
%F A166438 G.f.: (1+x)*(1-x^11)/(1 - 43*x + 945*x^11 - 903*x^12). (End)
%t A166438 With[{p=903, q=42}, 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 A166438 coxG[{11,903,-42}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 01 2022 *)
%o A166438 (Magma)
%o A166438 R<x>:=PowerSeriesRing(Integers(), 30);
%o A166438 f:= func< p,q,x | (1+x)*(1-x^11)/(1-(q+1)*x+(p+q)*x^11-p*x^12) >;
%o A166438 Coefficients(R!( f(903,42,x) )); // _G. C. Greubel_, Jul 26 2024
%o A166438 (SageMath)
%o A166438 def f(p,q,x): return (1+x)*(1-x^11)/(1-(q+1)*x+(p+q)*x^11-p*x^12)
%o A166438 def A166438_list(prec):
%o A166438     P.<x> = PowerSeriesRing(ZZ, prec)
%o A166438     return P( f(903,42,x) ).list()
%o A166438 A166438_list(30) # _G. C. Greubel_, Jul 26 2024
%Y A166438 Cf. A154638, A169452, A170763.
%K A166438 nonn
%O A166438 0,2
%A A166438 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009