cp's OEIS Frontend

A170460 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.

%I A170460 #9 Nov 21 2016 16:51:49
%S A170460 1,19,342,6156,110808,1994544,35901792,646232256,11632180608,
%T A170460 209379250944,3768826516992,67838877305856,1221099791505408,
%U A170460 21979796247097344,395636332447752192,7121453984059539456
%N A170460 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
%C A170460 The initial terms coincide with those of A170738, although the two sequences are eventually different.
%C A170460 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170460 <a href="/index/Rec#order_45">Index entries for linear recurrences with constant coefficients</a>, signature (17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, -153).
%F A170460 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 A170460 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 A170460 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 A170460 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 A170460 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 A170460 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(153*t^45 - 17*t^44 - 17*t^43 -
%F A170460 17*t^42 - 17*t^41 - 17*t^40 - 17*t^39 - 17*t^38 - 17*t^37 - 17*t^36 -
%F A170460 17*t^35 - 17*t^34 - 17*t^33 - 17*t^32 - 17*t^31 - 17*t^30 - 17*t^29 -
%F A170460 17*t^28 - 17*t^27 - 17*t^26 - 17*t^25 - 17*t^24 - 17*t^23 - 17*t^22 -
%F A170460 17*t^21 - 17*t^20 - 17*t^19 - 17*t^18 - 17*t^17 - 17*t^16 - 17*t^15 -
%F A170460 17*t^14 - 17*t^13 - 17*t^12 - 17*t^11 - 17*t^10 - 17*t^9 - 17*t^8 -
%F A170460 17*t^7 - 17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1)
%t A170460 With[{num=Total[2t^Range[44]]+t^45+1,den=Total[-17 t^Range[44]]+ 153t^45+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Sep 15 2011 *)
%K A170460 nonn
%O A170460 0,2
%A A170460 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009