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A169436 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169436 #13 May 08 2018 01:06:31
%S A169436 1,39,1482,56316,2140008,81320304,3090171552,117426518976,
%T A169436 4462207721088,169563893401344,6443427949251072,244850262071540736,
%U A169436 9304309958718547968,353563778431304822784,13435423580389583265792
%N A169436 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169436 The initial terms coincide with those of A170758, although the two sequences are eventually different.
%C A169436 First disagreement is at index 32, the difference is 741. - _Klaus Brockhaus_, Jun 30 2011
%C A169436 Computed with Magma using commands similar to those used to compute A154638.
%H A169436 <a href="/index/Rec#order_32">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, -703).
%F A169436 G.f.: (t^32 + 2*t^31 + 2*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^32 - 37*t^31 - 37*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).
%F A169436 G.f.: (1+2*sum(k=1..31,x^k)+x^32)/(1-37*sum(k=1..31,x^k)+703*x^32).
%t A169436 coxG[{32,703,-37}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 21 2016 *)
%Y A169436 Cf. A170758 (G.f.: (1+x)/(1-38*x) ).
%K A169436 nonn
%O A169436 0,2
%A A169436 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009