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A168703 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

%I A168703 #11 Nov 24 2016 13:08:07
%S A168703 1,26,650,16250,406250,10156250,253906250,6347656250,158691406250,
%T A168703 3967285156250,99182128906250,2479553222656250,61988830566406250,
%U A168703 1549720764160156250,38743019104003906250,968575477600097656250
%N A168703 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.
%C A168703 The initial terms coincide with those of A170745, although the two sequences are eventually different.
%C A168703 First disagreement at index 17: a(17) = 605359673500061035155925, A170745(17) = 605359673500061035156250. - _Klaus Brockhaus_, Mar 30 2011
%C A168703 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168703 G. C. Greubel, <a href="/A168703/b168703.txt">Table of n, a(n) for n = 0..500</a>
%H A168703 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, -300).
%F A168703 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)/(300*t^17 - 24*t^16 - 24*t^15 - 24*t^14 - 24*t^13 - 24*t^12 - 24*t^11 - 24*t^10 - 24*t^9 - 24*t^8 - 24*t^7 - 24*t^6 - 24*t^5 - 24*t^4 - 24*t^3 - 24*t^2 - 24*t + 1).
%t A168703 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)/(300*t^17 - 24*t^16 - 24*t^15 - 24*t^14 - 24*t^13 - 24*t^12 - 24*t^11 - 24*t^10 - 24*t^9 - 24*t^8 - 24*t^7 - 24*t^6 - 24*t^5 - 24*t^4 - 24*t^3 - 24*t^2 - 24*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Aug 04 2016 *)
%Y A168703 Cf. A170745 (G.f.: (1+x)/(1-25*x)).
%K A168703 nonn
%O A168703 0,2
%A A168703 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009