cp's OEIS Frontend

A170268 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.

%I A170268 #8 Nov 22 2016 11:46:58
%S A170268 1,19,342,6156,110808,1994544,35901792,646232256,11632180608,
%T A170268 209379250944,3768826516992,67838877305856,1221099791505408,
%U A170268 21979796247097344,395636332447752192,7121453984059539456
%N A170268 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
%C A170268 The initial terms coincide with those of A170738, although the two sequences are eventually different.
%C A170268 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170268 <a href="/index/Rec#order_41">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, -153).
%F A170268 G.f. (t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170268 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A170268 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +
%F A170268 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +
%F A170268 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170268 1)/(153*t^41 - 17*t^40 - 17*t^39 - 17*t^38 - 17*t^37 - 17*t^36 - 17*t^35
%F A170268 - 17*t^34 - 17*t^33 - 17*t^32 - 17*t^31 - 17*t^30 - 17*t^29 - 17*t^28 -
%F A170268 17*t^27 - 17*t^26 - 17*t^25 - 17*t^24 - 17*t^23 - 17*t^22 - 17*t^21 -
%F A170268 17*t^20 - 17*t^19 - 17*t^18 - 17*t^17 - 17*t^16 - 17*t^15 - 17*t^14 -
%F A170268 17*t^13 - 17*t^12 - 17*t^11 - 17*t^10 - 17*t^9 - 17*t^8 - 17*t^7 -
%F A170268 17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1)
%t A170268 With[{num=Total[2t^Range[40]]+t^41+1,den=Total[-17 t^Range[40]]+153t^41+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Mar 20 2013 *)
%K A170268 nonn
%O A170268 0,2
%A A170268 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009