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A170210 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.

%I A170210 #9 Nov 22 2016 15:14:14
%S A170210 1,9,72,576,4608,36864,294912,2359296,18874368,150994944,1207959552,
%T A170210 9663676416,77309411328,618475290624,4947802324992,39582418599936,
%U A170210 316659348799488,2533274790395904,20266198323167232,162129586585337856
%N A170210 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
%C A170210 The initial terms coincide with those of A003951, although the two sequences are eventually different.
%C A170210 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170210 <a href="/index/Rec#order_40">Index entries for linear recurrences with constant coefficients</a>, signature (7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, -28).
%F A170210 G.f. (t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 +
%F A170210 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 +
%F A170210 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 +
%F A170210 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 +
%F A170210 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170210 1)/(28*t^40 - 7*t^39 - 7*t^38 - 7*t^37 - 7*t^36 - 7*t^35 - 7*t^34 -
%F A170210 7*t^33 - 7*t^32 - 7*t^31 - 7*t^30 - 7*t^29 - 7*t^28 - 7*t^27 - 7*t^26 -
%F A170210 7*t^25 - 7*t^24 - 7*t^23 - 7*t^22 - 7*t^21 - 7*t^20 - 7*t^19 - 7*t^18 -
%F A170210 7*t^17 - 7*t^16 - 7*t^15 - 7*t^14 - 7*t^13 - 7*t^12 - 7*t^11 - 7*t^10 -
%F A170210 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1)
%t A170210 With[{num=Total[2t^Range[39]]+t^40+1,den=Total[-7 t^Range[39]]+ 28t^40+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Nov 01 2011 *)
%K A170210 nonn
%O A170210 0,2
%A A170210 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009