cp's OEIS Frontend

A170306 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

%I A170306 #9 Nov 22 2016 08:04:35
%S A170306 1,9,72,576,4608,36864,294912,2359296,18874368,150994944,1207959552,
%T A170306 9663676416,77309411328,618475290624,4947802324992,39582418599936,
%U A170306 316659348799488,2533274790395904,20266198323167232,162129586585337856
%N A170306 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
%C A170306 The initial terms coincide with those of A003951, although the two sequences are eventually different.
%C A170306 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170306 <a href="/index/Rec#order_42">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, -28).
%F A170306 G.f. (t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +
%F A170306 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 A170306 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 A170306 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 A170306 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 A170306 2*t + 1)/(28*t^42 - 7*t^41 - 7*t^40 - 7*t^39 - 7*t^38 - 7*t^37 - 7*t^36
%F A170306 - 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 A170306 - 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 A170306 - 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 A170306 - 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 A170306 7*t^3 - 7*t^2 - 7*t + 1)
%t A170306 With[{num=Total[2t^Range[41]]+t^42+1,den=Total[-7 t^Range[41]]+28t^42+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Sep 28 2011 *)
%K A170306 nonn
%O A170306 0,2
%A A170306 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009