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A165654 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I. 0

%I #9 Nov 23 2016 22:15:49

%S 1,37,1332,47952,1726272,62145792,2237248512,80540946432,

%T 2899474071552,104381066575206,3757718396683440,135277862279741370,

%U 4870003042039640400,175320109512309293280,6311523942402895157760

%N Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

%C The initial terms coincide with those of A170756, although the two sequences are eventually different.

%C Computed with MAGMA using commands similar to those used to compute A154638.

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (35, 35, 35, 35, 35, 35, 35, 35, -630).

%F G.f. (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 +

%F 1)/(630*t^9 - 35*t^8 - 35*t^7 - 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 -

%F 35*t^2 - 35*t + 1)

%t With[{num=Total[2t^Range[8]]+t^9+1,den=Total[-35 t^Range[8]]+ 630t^9+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Nov 01 2011 *)

%K nonn

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)