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A169550 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

%I A169550 #8 May 14 2018 09:40:06
%S A169550 1,9,72,576,4608,36864,294912,2359296,18874368,150994944,1207959552,
%T A169550 9663676416,77309411328,618475290624,4947802324992,39582418599936,
%U A169550 316659348799488,2533274790395904,20266198323167232,162129586585337856
%N A169550 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
%C A169550 The initial terms coincide with those of A003951, although the two sequences are eventually different.
%C A169550 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169550 <a href="/index/Rec#order_35">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, -28).
%F A169550 G.f. (t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A169550 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 A169550 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 A169550 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 A169550 + 2*t^2 + 2*t + 1)/(28*t^35 - 7*t^34 - 7*t^33 - 7*t^32 - 7*t^31 - 7*t^30
%F A169550 - 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 A169550 - 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 A169550 - 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 A169550 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1)
%t A169550 coxG[{35,28,-7}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 14 2018 *)
%K A169550 nonn
%O A169550 0,2
%A A169550 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009