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A170450 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.

%I A170450 #8 Apr 24 2022 15:44:28
%S A170450 1,9,72,576,4608,36864,294912,2359296,18874368,150994944,1207959552,
%T A170450 9663676416,77309411328,618475290624,4947802324992,39582418599936,
%U A170450 316659348799488,2533274790395904,20266198323167232,162129586585337856
%N A170450 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
%C A170450 The initial terms coincide with those of A003951, although the two sequences are eventually different.
%C A170450 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170450 <a href="/index/Rec#order_45">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, 7, 7, -28).
%F A170450 G.f. (t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 +
%F A170450 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 +
%F A170450 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 +
%F A170450 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 +
%F A170450 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 +
%F A170450 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(28*t^45 - 7*t^44 - 7*t^43 -
%F A170450 7*t^42 - 7*t^41 - 7*t^40 - 7*t^39 - 7*t^38 - 7*t^37 - 7*t^36 - 7*t^35 -
%F A170450 7*t^34 - 7*t^33 - 7*t^32 - 7*t^31 - 7*t^30 - 7*t^29 - 7*t^28 - 7*t^27 -
%F A170450 7*t^26 - 7*t^25 - 7*t^24 - 7*t^23 - 7*t^22 - 7*t^21 - 7*t^20 - 7*t^19 -
%F A170450 7*t^18 - 7*t^17 - 7*t^16 - 7*t^15 - 7*t^14 - 7*t^13 - 7*t^12 - 7*t^11 -
%F A170450 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 -
%F A170450 7*t + 1)
%t A170450 coxG[{45,28,-7}] (* The coxG program is at A169452 *)  (* _Harvey P. Dale_, Apr 24 2022 *)
%K A170450 nonn
%O A170450 0,2
%A A170450 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009