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A168734 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

%I A168734 #12 Nov 24 2016 13:51:37
%S A168734 1,9,72,576,4608,36864,294912,2359296,18874368,150994944,1207959552,
%T A168734 9663676416,77309411328,618475290624,4947802324992,39582418599936,
%U A168734 316659348799488,2533274790395904,20266198323167196,162129586585337280
%N A168734 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.
%C A168734 The initial terms coincide with those of A003951, although the two sequences are eventually different.
%C A168734 First disagreement at index 18: a(18) = 20266198323167196, A003951(18) = 20266198323167232. - _Klaus Brockhaus_, Mar 27 2011
%C A168734 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168734 G. C. Greubel, <a href="/A168734/b168734.txt">Table of n, a(n) for n = 0..500</a>
%H A168734 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, -28).
%F A168734 G.f.: (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)/(28*t^18 - 7*t^17 - 7*t^16 - 7*t^15 - 7*t^14 - 7*t^13 - 7*t^12 - 7*t^11 - 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1).
%t A168734 CoefficientList[Series[(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)/(28*t^18 - 7*t^17 - 7*t^16 - 7*t^15 - 7*t^14 - 7*t^13 - 7*t^12 - 7*t^11 - 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Aug 08 2016 *)
%Y A168734 Cf. A003951 (G.f.: (1+x)/(1-8*x)).
%K A168734 nonn,easy
%O A168734 0,2
%A A168734 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009