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A168707 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

%I A168707 #13 Sep 09 2019 09:57:50
%S A168707 1,30,870,25230,731670,21218430,615334470,17844699630,517496289270,
%T A168707 15007392388830,435214379276070,12621216999006030,366015292971174870,
%U A168707 10614443496164071230,307818861388758065670,8926746980273983904430
%N A168707 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.
%C A168707 The initial terms coincide with those of A170749, although the two sequences are eventually different.
%C A168707 First disagreement at index 17: a(17) = 7507394210410420463625195, A170749(17) = 7507394210410420463625630. - _Klaus Brockhaus_, Mar 28 2011
%C A168707 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168707 G. C. Greubel, <a href="/A168707/b168707.txt">Table of n, a(n) for n = 0..500</a>
%H A168707 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, -406).
%F A168707 G.f.: (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)/(406*t^17 - 28*t^16 - 28*t^15 - 28*t^14 - 28*t^13 - 28*t^12 - 28*t^11 - 28*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).
%t A168707 CoefficientList[Series[(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)/(406*t^17 - 28*t^16 - 28*t^15 - 28*t^14 - 28*t^13 - 28*t^12 - 28*t^11 - 28*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Aug 04 2016 *)
%t A168707 coxG[{17,46,-28}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 09 2019 *)
%Y A168707 Cf. A170749 (G.f.: (1+x)/(1-29*x)).
%K A168707 nonn
%O A168707 0,2
%A A168707 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009