A169320 - OEIS

%I #12 May 10 2018 01:23:17

%S 1,19,342,6156,110808,1994544,35901792,646232256,11632180608,

%T 209379250944,3768826516992,67838877305856,1221099791505408,

%U 21979796247097344,395636332447752192,7121453984059539456

%N Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.

%C The initial terms coincide with those of A170738, although the two sequences are eventually different.

%C First disagreement at index 30: a(30) = 48045890697231303708893365599303892821, A170738(30) = 48045890697231303708893365599303892992. - _Klaus Brockhaus_, Jun 22 2011

%C Computed with Magma using commands similar to those used to compute A154638.

%H <a href="/index/Rec#order_30">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, -153).

%F G.f.: (t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 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 + 2*t + 1)/(153*t^30 - 17*t^29 - 17*t^28 - 17*t^27 - 17*t^26 - 17*t^25 - 17*t^24 - 17*t^23 - 17*t^22 - 17*t^21 - 17*t^20 - 17*t^19 - 17*t^18 - 17*t^17 - 17*t^16 - 17*t^15 - 17*t^14 - 17*t^13 - 17*t^12 - 17*t^11 - 17*t^10 - 17*t^9 - 17*t^8 - 17*t^7 - 17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1).

%t coxG[{30,153,-17}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Feb 10 2016 *)

%Y Cf. A170738 (G.f.: (1+x)/(1-18*x)).

%K nonn

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009