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A168737 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

%I A168737 #14 Jul 10 2023 13:03:09
%S A168737 1,12,132,1452,15972,175692,1932612,21258732,233846052,2572306572,
%T A168737 28295372292,311249095212,3423740047332,37661140520652,
%U A168737 414272545727172,4556998002998892,50126978032987812,551396758362865932
%N A168737 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.
%C A168737 The initial terms coincide with those of A003954, although the two sequences are eventually different.
%C A168737 First disagreement at index 18: a(18) = 6065364341991525186, A003954(18) = 6065364341991525252. - _Klaus Brockhaus_, Mar 27 2011
%C A168737 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168737 G. C. Greubel, <a href="/A168737/b168737.txt">Table of n, a(n) for n = 0..500</a>
%H A168737 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, -55).
%F A168737 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)/(55*t^18 - 10*t^17 - 10*t^16 - 10*t^15 - 10*t^14 - 10*t^13 - 10*t^12 - 10*t^11 - 10*t^10 - 10*t^9 - 10*t^8 - 10*t^7 - 10*t^6 - 10*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1).
%t A168737 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)/(55*t^18 - 10*t^17 - 10*t^16 - 10*t^15 - 10*t^14 - 10*t^13 - 10*t^12 - 10*t^11 - 10*t^10 - 10*t^9 - 10*t^8 - 10*t^7 - 10*t^6 - 10*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Aug 08 2016 *)
%t A168737 coxG[{18,55,-10}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 10 2023 *)
%Y A168737 Cf. A003954 (G.f.: (1+x)/(1-11*x)).
%K A168737 nonn,easy
%O A168737 0,2
%A A168737 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009