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A169319 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.

%I A169319 #12 Nov 07 2021 19:23:55
%S A169319 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,
%T A169319 125563633938,2134581776946,36287890208082,616894133537394,
%U A169319 10487200270135698,178282404592306866,3030800878069216722,51523614927176684274
%N A169319 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
%C A169319 The initial terms coincide with those of A170737, although the two sequences are eventually different.
%C A169319 First disagreement at index 30: a(30) = 8675434297921516471645412854015290393, A170737(30) = 8675434297921516471645412854015290546. - _Klaus Brockhaus_, Jun 22 2011
%C A169319 Computed with Magma using commands similar to those used to compute A154638.
%H A169319 <a href="/index/Rec#order_30">Index entries for linear recurrences with constant coefficients</a>, signature (16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, -136).
%F A169319 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)/(136*t^30 - 16*t^29 - 16*t^28 - 16*t^27 - 16*t^26 - 16*t^25 - 16*t^24 - 16*t^23 - 16*t^22 - 16*t^21 - 16*t^20 - 16*t^19 - 16*t^18 - 16*t^17 - 16*t^16 - 16*t^15 - 16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1).
%t A169319 coxG[{30,136,-16}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Nov 07 2021 *)
%Y A169319 Cf. A170737 (G.f.: (1+x)/(1-17*x)).
%K A169319 nonn
%O A169319 0,2
%A A169319 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009