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A168742 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

%I A168742 #16 Dec 26 2017 16:55:47
%S A168742 1,17,272,4352,69632,1114112,17825792,285212672,4563402752,
%T A168742 73014444032,1168231104512,18691697672192,299067162755072,
%U A168742 4785074604081152,76561193665298432,1224979098644774912,19599665578316398592
%N A168742 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.
%C A168742 The initial terms coincide with those of A170736, although the two sequences are eventually different.
%C A168742 First disagreement at index 18: a(18) = 5017514388048998039416, A170736(18) = 5017514388048998039552. - _Klaus Brockhaus_, Mar 27 2011
%C A168742 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168742 G. C. Greubel, <a href="/A168742/b168742.txt">Table of n, a(n) for n = 0..500</a>
%H A168742 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, -120).
%F A168742 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)/(120*t^18 - 15*t^17 - 15*t^16 - 15*t^15 - 15*t^14 - 15*t^13 - 15*t^12 - 15*t^11 - 15*t^10 - 15*t^9 - 15*t^8 - 15*t^7 - 15*t^6 - 15*t^5 - 15*t^4 - 15*t^3 - 15*t^2 - 15*t + 1).
%t A168742 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)/(120*t^18 - 15*t^17 - 15*t^16 - 15*t^15 - 15*t^14 - 15*t^13 - 15*t^12 - 15*t^11 - 15*t^10 - 15*t^9 - 15*t^8 - 15*t^7 - 15*t^6 - 15*t^5 - 15*t^4 - 15*t^3 - 15*t^2 - 15*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 10 2016 *)
%t A168742 coxG[{18,120,-15}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 26 2017 *)
%Y A168742 Cf. A170736 (G.f.: (1+x)/(1-16*x)).
%K A168742 nonn,easy
%O A168742 0,2
%A A168742 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009