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A169340 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.

%I A169340 #12 May 10 2018 00:28:38
%S A169340 1,39,1482,56316,2140008,81320304,3090171552,117426518976,
%T A169340 4462207721088,169563893401344,6443427949251072,244850262071540736,
%U A169340 9304309958718547968,353563778431304822784,13435423580389583265792
%N A169340 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
%C A169340 The initial terms coincide with those of A170758, although the two sequences are eventually different.
%C A169340 First disagreement at index 30: a(30) = 253973795268678209284064940544087321691314715931, A170758(30) = 253973795268678209284064940544087321691314716672. - _Klaus Brockhaus_, Jun 23 2011
%C A169340 Computed with Magma using commands similar to those used to compute A154638.
%H A169340 <a href="/index/Rec#order_30">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, -703).
%F A169340 G.f.: (t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 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 + 2*t^2 + 2*t + 1)/(703*t^30 - 37*t^29 - 37*t^28 - 37*t^27 - 37*t^26 - 37*t^25 - 37*t^24 - 37*t^23 - 37*t^22 - 37*t^21 - 37*t^20 - 37*t^19 - 37*t^18 - 37*t^17 - 37*t^16 - 37*t^15 - 37*t^14 - 37*t^13 - 37*t^12 - 37*t^11 - 37*t^10 - 37*t^9 - 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 A169340 coxG[{30,703,-37}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 30 2016 *)
%Y A169340 Cf. A170758 (G.f.: (1+x)/(1-38*x)).
%K A169340 nonn
%O A169340 0,2
%A A169340 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009