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A166432 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%I A166432 #15 Jul 25 2024 23:06:01
%S A166432 1,38,1406,52022,1924814,71218118,2635070366,97497603542,
%T A166432 3607411331054,133474219248998,4938546112212926,182726206151877559,
%U A166432 6760869627619443672,250152176221918454160,9255630520210947220872
%N A166432 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166432 The initial terms coincide with those of A170757, although the two sequences are eventually different.
%C A166432 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166432 G. C. Greubel, <a href="/A166432/b166432.txt">Table of n, a(n) for n = 0..500</a>
%H A166432 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (36,36,36,36,36,36,36,36,36,36,-666).
%F A166432 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)/(666*t^11 - 36*t^10 - 36*t^9 - 36*t^8 - 36*t^7 - 36*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1).
%F A166432 From _G. C. Greubel_, Jul 25 2024: (Start)
%F A166432 a(n) = 26*Sum_{j=1..10} a(n-j) - 351*a(n-11).
%F A166432 G.f.: (1+x)*(1-x^11)/(1 - 37*x + 702*x^11 - 666*x^12). (End)
%t A166432 With[{p=666, q=36}, 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 25 2024 *)
%t A166432 coxG[{11,666,-36}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 26 2016 *)
%o A166432 (Magma)
%o A166432 R<x>:=PowerSeriesRing(Integers(), 30);
%o A166432 Coefficients(R!( (1+x)*(1-x^11)/(1-37*x+702*x^11-666*x^12) )); // _G. C. Greubel_, Jul 25 2024
%o A166432 (SageMath)
%o A166432 def A166432_list(prec):
%o A166432     P.<x> = PowerSeriesRing(ZZ, prec)
%o A166432     return P( (1+x)*(1-x^11)/(1-37*x+702*x^11-666*x^12) ).list()
%o A166432 A166432_list(30) # _G. C. Greubel_, Jul 25 2024
%Y A166432 Cf. A154638, A169452, A170757.
%K A166432 nonn
%O A166432 0,2
%A A166432 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009