cp's OEIS Frontend

A170594 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.

%I A170594 #8 Nov 21 2016 12:02:36
%S A170594 1,9,72,576,4608,36864,294912,2359296,18874368,150994944,1207959552,
%T A170594 9663676416,77309411328,618475290624,4947802324992,39582418599936,
%U A170594 316659348799488,2533274790395904,20266198323167232,162129586585337856
%N A170594 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
%C A170594 The initial terms coincide with those of A003951, although the two sequences are eventually different.
%C A170594 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170594 <a href="/index/Rec#order_48">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, -28).
%F A170594 G.f. (t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 +
%F A170594 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 +
%F A170594 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 +
%F A170594 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 +
%F A170594 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 +
%F A170594 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170594 1)/(28*t^48 - 7*t^47 - 7*t^46 - 7*t^45 - 7*t^44 - 7*t^43 - 7*t^42 -
%F A170594 7*t^41 - 7*t^40 - 7*t^39 - 7*t^38 - 7*t^37 - 7*t^36 - 7*t^35 - 7*t^34 -
%F A170594 7*t^33 - 7*t^32 - 7*t^31 - 7*t^30 - 7*t^29 - 7*t^28 - 7*t^27 - 7*t^26 -
%F A170594 7*t^25 - 7*t^24 - 7*t^23 - 7*t^22 - 7*t^21 - 7*t^20 - 7*t^19 - 7*t^18 -
%F A170594 7*t^17 - 7*t^16 - 7*t^15 - 7*t^14 - 7*t^13 - 7*t^12 - 7*t^11 - 7*t^10 -
%F A170594 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1)
%t A170594 With[{num=Total[2t^Range[47]]+t^48+1,den=Total[-7 t^Range[47]]+28t^48+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Apr 07 2013 *)
%K A170594 nonn
%O A170594 0,2
%A A170594 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009