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A170690 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170690 #12 Feb 28 2022 20:09:49
%S A170690 1,9,72,576,4608,36864,294912,2359296,18874368,150994944,1207959552,
%T A170690 9663676416,77309411328,618475290624,4947802324992,39582418599936,
%U A170690 316659348799488,2533274790395904,20266198323167232,162129586585337856
%N A170690 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170690 The initial terms coincide with those of A003951, although the two sequences are eventually different.
%C A170690 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170690 About the initial comment, first disagreement is at index 50 and the difference is 36. - _Vincenzo Librandi_, Dec 09 2012
%H A170690 Vincenzo Librandi, <a href="/A170690/b170690.txt">Table of n, a(n) for n = 0..200</a>
%H A170690 <a href="/index/Rec#order_50">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, 7, 7, 7, -28).
%F A170690 G.f. (t^50 + 2*t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 +
%F A170690 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +
%F A170690 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A170690 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A170690 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A170690 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 +
%F A170690 2*t + 1)/(28*t^50 - 7*t^49 - 7*t^48 - 7*t^47 - 7*t^46 - 7*t^45 - 7*t^44
%F A170690 - 7*t^43 - 7*t^42 - 7*t^41 - 7*t^40 - 7*t^39 - 7*t^38 - 7*t^37 - 7*t^36
%F A170690 - 7*t^35 - 7*t^34 - 7*t^33 - 7*t^32 - 7*t^31 - 7*t^30 - 7*t^29 - 7*t^28
%F A170690 - 7*t^27 - 7*t^26 - 7*t^25 - 7*t^24 - 7*t^23 - 7*t^22 - 7*t^21 - 7*t^20
%F A170690 - 7*t^19 - 7*t^18 - 7*t^17 - 7*t^16 - 7*t^15 - 7*t^14 - 7*t^13 - 7*t^12
%F A170690 - 7*t^11 - 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 -
%F A170690 7*t^3 - 7*t^2 - 7*t + 1)
%t A170690 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-7 t^Range[49]] + 28 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* _Vincenzo Librandi_, Dec 09 2012 *)
%t A170690 coxG[{50,28,-7}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Feb 28 2022 *)
%K A170690 nonn
%O A170690 0,2
%A A170690 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009