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A170000 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I. 0

%I

%S 1,39,1482,56316,2140008,81320304,3090171552,117426518976,

%T 4462207721088,169563893401344,6443427949251072,244850262071540736,

%U 9304309958718547968,353563778431304822784,13435423580389583265792

%N Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

%C The initial terms coincide with those of A170758, 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_35">Index entries for linear recurrences with constant coefficients</a>, signature (37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, -703).

%F G.f. (t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +

%F 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 +

%F 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 +

%F 2*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

%F + 2*t^2 + 2*t + 1)/(703*t^35 - 37*t^34 - 37*t^33 - 37*t^32 - 37*t^31 -

%F 37*t^30 - 37*t^29 - 37*t^28 - 37*t^27 - 37*t^26 - 37*t^25 - 37*t^24 -

%F 37*t^23 - 37*t^22 - 37*t^21 - 37*t^20 - 37*t^19 - 37*t^18 - 37*t^17 -

%F 37*t^16 - 37*t^15 - 37*t^14 - 37*t^13 - 37*t^12 - 37*t^11 - 37*t^10 -

%F 37*t^9 - 37*t^8 - 37*t^7 - 37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 - 37*t^2 -

%F 37*t + 1)

%t With[{num=Total[2t^Range[34]]+t^35+1,den=Total[-37 t^Range[34]]+ 703t^35+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jan 20 2013 *)

%K nonn

%O 0,2

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

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Last modified September 24 07:01 EDT 2020. Contains 337317 sequences. (Running on oeis4.)