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%I A170354 #6 Nov 21 2016 19:14:12
%S A170354 1,9,72,576,4608,36864,294912,2359296,18874368,150994944,1207959552,
%T A170354 9663676416,77309411328,618475290624,4947802324992,39582418599936,
%U A170354 316659348799488,2533274790395904,20266198323167232,162129586585337856
%N A170354 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
%C A170354 The initial terms coincide with those of A003951, although the two sequences are eventually different.
%C A170354 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170354 <a href="/index/Rec#order_43">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, 7, 7, 7, -28).
%F A170354 G.f. (t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 +
%F A170354 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A170354 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 +
%F A170354 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 +
%F A170354 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
%F A170354 + 2*t^2 + 2*t + 1)/(28*t^43 - 7*t^42 - 7*t^41 - 7*t^40 - 7*t^39 - 7*t^38
%F A170354 - 7*t^37 - 7*t^36 - 7*t^35 - 7*t^34 - 7*t^33 - 7*t^32 - 7*t^31 - 7*t^30
%F A170354 - 7*t^29 - 7*t^28 - 7*t^27 - 7*t^26 - 7*t^25 - 7*t^24 - 7*t^23 - 7*t^22
%F A170354 - 7*t^21 - 7*t^20 - 7*t^19 - 7*t^18 - 7*t^17 - 7*t^16 - 7*t^15 - 7*t^14
%F A170354 - 7*t^13 - 7*t^12 - 7*t^11 - 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 -
%F A170354 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1)
%K A170354 nonn
%O A170354 0,2
%A A170354 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009

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