cp's OEIS Frontend

A170172 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.

%I A170172 #8 Nov 22 2016 15:49:58
%S A170172 1,19,342,6156,110808,1994544,35901792,646232256,11632180608,
%T A170172 209379250944,3768826516992,67838877305856,1221099791505408,
%U A170172 21979796247097344,395636332447752192,7121453984059539456
%N A170172 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
%C A170172 The initial terms coincide with those of A170738, although the two sequences are eventually different.
%C A170172 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170172 <a href="/index/Rec#order_39">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, -153).
%F A170172 G.f. (t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 +
%F A170172 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 +
%F A170172 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 +
%F A170172 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 +
%F A170172 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(153*t^39 -
%F A170172 17*t^38 - 17*t^37 - 17*t^36 - 17*t^35 - 17*t^34 - 17*t^33 - 17*t^32 -
%F A170172 17*t^31 - 17*t^30 - 17*t^29 - 17*t^28 - 17*t^27 - 17*t^26 - 17*t^25 -
%F A170172 17*t^24 - 17*t^23 - 17*t^22 - 17*t^21 - 17*t^20 - 17*t^19 - 17*t^18 -
%F A170172 17*t^17 - 17*t^16 - 17*t^15 - 17*t^14 - 17*t^13 - 17*t^12 - 17*t^11 -
%F A170172 17*t^10 - 17*t^9 - 17*t^8 - 17*t^7 - 17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 -
%F A170172 17*t^2 - 17*t + 1)
%t A170172 coxG[{39,153,-17}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 03 2016 *)
%K A170172 nonn
%O A170172 0,2
%A A170172 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009