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A170144 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.

%I A170144 #8 May 14 2017 17:41:02
%S A170144 1,39,1482,56316,2140008,81320304,3090171552,117426518976,
%T A170144 4462207721088,169563893401344,6443427949251072,244850262071540736,
%U A170144 9304309958718547968,353563778431304822784,13435423580389583265792
%N A170144 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
%C A170144 The initial terms coincide with those of A170758, although the two sequences are eventually different.
%C A170144 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170144 <a href="/index/Rec#order_38">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, 37, 37, 37, -703).
%F A170144 G.f. (t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 +
%F A170144 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 +
%F A170144 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 +
%F A170144 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 +
%F A170144 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(703*t^38 - 37*t^37 -
%F A170144 37*t^36 - 37*t^35 - 37*t^34 - 37*t^33 - 37*t^32 - 37*t^31 - 37*t^30 -
%F A170144 37*t^29 - 37*t^28 - 37*t^27 - 37*t^26 - 37*t^25 - 37*t^24 - 37*t^23 -
%F A170144 37*t^22 - 37*t^21 - 37*t^20 - 37*t^19 - 37*t^18 - 37*t^17 - 37*t^16 -
%F A170144 37*t^15 - 37*t^14 - 37*t^13 - 37*t^12 - 37*t^11 - 37*t^10 - 37*t^9 -
%F A170144 37*t^8 - 37*t^7 - 37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1)
%t A170144 coxG[{38,703,-37}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 04 2014 *)
%K A170144 nonn
%O A170144 0,2
%A A170144 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009