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A166440 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%I A166440 #14 Jul 26 2024 05:29:06
%S A166440 1,46,2070,93150,4191750,188628750,8488293750,381973218750,
%T A166440 17188794843750,773495767968750,34807309558593750,1566328930136717715,
%U A166440 70484801856152250600,3171816083526849182160,142731723758708118929400
%N A166440 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166440 The initial terms coincide with those of A170765, although the two sequences are eventually different.
%C A166440 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166440 G. C. Greubel, <a href="/A166440/b166440.txt">Table of n, a(n) for n = 0..500</a>
%H A166440 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (44,44,44,44,44,44,44,44,44,44,-990).
%F A166440 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)/(990*t^11 - 44*t^10 - 44*t^9 - 44*t^8 - 44*t^7 - 44*t^6 - 44*t^5 - 44*t^4 - 44*t^3 - 44*t^2 - 44*t + 1).
%F A166440 From _G. C. Greubel_, Jul 26 2024: (Start)
%F A166440 a(n) = 44*Sum_{j=1..10} a(n-j) - 990*a(n-11).
%F A166440 G.f.: (1+x)*(1-x^11)/(1 - 45*x + 1034*x^11 - 990*x^12). (End)
%t A166440 With[{p=990, q=44}, 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 A166440 coxG[{11, 990, -44, 30}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Jul 26 2024 *)
%o A166440 (Magma)
%o A166440 R<x>:=PowerSeriesRing(Integers(), 30);
%o A166440 f:= func< p,q,x | (1+x)*(1-x^11)/(1-(q+1)*x+(p+q)*x^11-p*x^12) >;
%o A166440 Coefficients(R!( f(990,44,x) )); // _G. C. Greubel_, Jul 26 2024
%o A166440 (SageMath)
%o A166440 def f(p,q,x): return (1+x)*(1-x^11)/(1-(q+1)*x+(p+q)*x^11-p*x^12)
%o A166440 def A166440_list(prec):
%o A166440     P.<x> = PowerSeriesRing(ZZ, prec)
%o A166440     return P( f(990,44,x) ).list()
%o A166440 A166440_list(30) # _G. C. Greubel_, Jul 26 2024
%Y A166440 Cf. A154638, A169452, A170765.
%K A166440 nonn
%O A166440 0,2
%A A166440 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009