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A168691 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

%I A168691 #16 Dec 22 2019 12:55:02
%S A168691 1,14,182,2366,30758,399854,5198102,67575326,878479238,11420230094,
%T A168691 148462991222,1930018885886,25090245516518,326173191714734,
%U A168691 4240251492291542,55123269399790046,716602502197270598
%N A168691 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.
%C A168691 The initial terms coincide with those of A170733, although the two sequences are eventually different.
%C A168691 First disagreement at index 17: a(17) = 9315832528564517683, A170733(17) = 9315832528564517774. - _Klaus Brockhaus_, Mar 30 2011
%C A168691 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168691 G. C. Greubel, <a href="/A168691/b168691.txt">Table of n, a(n) for n = 0..500</a>
%H A168691 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, -78).
%F A168691 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)/ (78*t^17 - 12*t^16 - 12*t^15 - 12*t^14 - 12*t^13 - 12*t^12 - 12*t^11 - 12*t^10 - 12*t^9 - 12*t^8 - 12*t^7 - 12*t^6 - 12*t^5 - 12*t^4 - 12*t^3 - 12*t^2 - 12*t + 1).
%t A168691 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)/(78*t^17 - 12*t^16 - 12*t^15 - 12*t^14 - 12*t^13 - 12*t^12 - 12*t^11 - 12*t^10 - 12*t^9 - 12*t^8 - 12*t^7 - 12*t^6 - 12*t^5 - 12*t^4 - 12*t^3 - 12*t^2 - 12*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Aug 03 2016 *)
%t A168691 coxG[{17,78,-12}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 22 2019 *)
%Y A168691 Cf. A170733 (G.f.: (1+x)/(1-13*x)).
%K A168691 nonn
%O A168691 0,2
%A A168691 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009