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A170546 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.

%I A170546 #8 Nov 21 2016 12:46:52
%S A170546 1,9,72,576,4608,36864,294912,2359296,18874368,150994944,1207959552,
%T A170546 9663676416,77309411328,618475290624,4947802324992,39582418599936,
%U A170546 316659348799488,2533274790395904,20266198323167232,162129586585337856
%N A170546 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
%C A170546 The initial terms coincide with those of A003951, although the two sequences are eventually different.
%C A170546 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170546 <a href="/index/Rec#order_47">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, 7, 7, -28).
%F A170546 G.f. (t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 +
%F A170546 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 +
%F A170546 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 +
%F A170546 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 +
%F A170546 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 +
%F A170546 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(28*t^47 -
%F A170546 7*t^46 - 7*t^45 - 7*t^44 - 7*t^43 - 7*t^42 - 7*t^41 - 7*t^40 - 7*t^39 -
%F A170546 7*t^38 - 7*t^37 - 7*t^36 - 7*t^35 - 7*t^34 - 7*t^33 - 7*t^32 - 7*t^31 -
%F A170546 7*t^30 - 7*t^29 - 7*t^28 - 7*t^27 - 7*t^26 - 7*t^25 - 7*t^24 - 7*t^23 -
%F A170546 7*t^22 - 7*t^21 - 7*t^20 - 7*t^19 - 7*t^18 - 7*t^17 - 7*t^16 - 7*t^15 -
%F A170546 7*t^14 - 7*t^13 - 7*t^12 - 7*t^11 - 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 -
%F A170546 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1)
%t A170546 coxG[{47,28,-7}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 16 2015 *)
%K A170546 nonn
%O A170546 0,2
%A A170546 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009