cp's OEIS Frontend

A170316 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

%I A170316 #6 Nov 22 2016 08:10:27
%S A170316 1,19,342,6156,110808,1994544,35901792,646232256,11632180608,
%T A170316 209379250944,3768826516992,67838877305856,1221099791505408,
%U A170316 21979796247097344,395636332447752192,7121453984059539456
%N A170316 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
%C A170316 The initial terms coincide with those of A170738, although the two sequences are eventually different.
%C A170316 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170316 <a href="/index/Rec#order_42">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, -153).
%F A170316 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 A170316 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 A170316 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 A170316 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 A170316 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 A170316 2*t + 1)/(153*t^42 - 17*t^41 - 17*t^40 - 17*t^39 - 17*t^38 - 17*t^37 -
%F A170316 17*t^36 - 17*t^35 - 17*t^34 - 17*t^33 - 17*t^32 - 17*t^31 - 17*t^30 -
%F A170316 17*t^29 - 17*t^28 - 17*t^27 - 17*t^26 - 17*t^25 - 17*t^24 - 17*t^23 -
%F A170316 17*t^22 - 17*t^21 - 17*t^20 - 17*t^19 - 17*t^18 - 17*t^17 - 17*t^16 -
%F A170316 17*t^15 - 17*t^14 - 17*t^13 - 17*t^12 - 17*t^11 - 17*t^10 - 17*t^9 -
%F A170316 17*t^8 - 17*t^7 - 17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1)
%K A170316 nonn
%O A170316 0,2
%A A170316 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009