cp's OEIS Frontend

A169052 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.

%I A169052 #10 Nov 25 2016 11:06:23
%S A169052 1,39,1482,56316,2140008,81320304,3090171552,117426518976,
%T A169052 4462207721088,169563893401344,6443427949251072,244850262071540736,
%U A169052 9304309958718547968,353563778431304822784,13435423580389583265792
%N A169052 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
%C A169052 The initial terms coincide with those of A170758, although the two sequences are eventually different.
%C A169052 First disagreement at index 24: a(24) = 84350435505142246566995199771078032667, A170758(24) = 84350435505142246566995199771078033408. - Klaus Brockhaus, Apr 20 2011
%C A169052 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169052 <a href="/index/Rec#order_24">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, -703).
%F A169052 G.f.: (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^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 A169052 coxG[{24,703,-37}] (* See A169452 for the coxG program *) (* _Harvey P. Dale_, Sep 23 2014 *)
%Y A169052 Cf. A170758 (G.f.: (1+x)/(1-38*x)).
%K A169052 nonn
%O A169052 0,2
%A A169052 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009