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A170507 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.

%I A170507 #8 Nov 21 2016 14:06:16
%S A170507 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,
%T A170507 125563633938,2134581776946,36287890208082,616894133537394,
%U A170507 10487200270135698,178282404592306866,3030800878069216722,51523614927176684274
%N A170507 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
%C A170507 The initial terms coincide with those of A170737, although the two sequences are eventually different.
%C A170507 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170507 <a href="/index/Rec#order_46">Index entries for linear recurrences with constant coefficients</a>, signature (16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, -136).
%F A170507 G.f. (t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 +
%F A170507 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 +
%F A170507 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 +
%F A170507 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 +
%F A170507 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 +
%F A170507 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(136*t^46 - 16*t^45 -
%F A170507 16*t^44 - 16*t^43 - 16*t^42 - 16*t^41 - 16*t^40 - 16*t^39 - 16*t^38 -
%F A170507 16*t^37 - 16*t^36 - 16*t^35 - 16*t^34 - 16*t^33 - 16*t^32 - 16*t^31 -
%F A170507 16*t^30 - 16*t^29 - 16*t^28 - 16*t^27 - 16*t^26 - 16*t^25 - 16*t^24 -
%F A170507 16*t^23 - 16*t^22 - 16*t^21 - 16*t^20 - 16*t^19 - 16*t^18 - 16*t^17 -
%F A170507 16*t^16 - 16*t^15 - 16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 -
%F A170507 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 -
%F A170507 16*t + 1)
%t A170507 With[{num=Total[2t^Range[45]]+t^46+1,den=Total[-16 t^Range[45]]+136t^46+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Aug 23 2013 *)
%K A170507 nonn
%O A170507 0,2
%A A170507 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009