A168812 - OEIS

%I #14 Feb 13 2018 13:16:27

%S 1,39,1482,56316,2140008,81320304,3090171552,117426518976,

%T 4462207721088,169563893401344,6443427949251072,244850262071540736,

%U 9304309958718547968,353563778431304822784,13435423580389583265792

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

%C The initial terms coincide with those of A170758, although the two sequences are eventually different.

%C First disagreement at index 19: a(19) = 1064558044543330135515017772315, A170758(19) = 1064558044543330135515017773056. - _Klaus Brockhaus_, Apr 01 2011

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

%H G. C. Greubel, <a href="/A168812/b168812.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, -703).

%F G.f.: (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)/(703*t^19 - 37*t^18 - 37*t^17 - 37*t^16 - 37*t^15 - 37*t^14 - 37*t^13 - 37*t^12 - 37*t^11 - 37*t^10 - 37*t^9 - 37*t^8 - 37*t^7 - 37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1).

%t CoefficientList[Series[(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)/(703*t^19 - 37*t^18 - 37*t^17 - 37*t^16 - 37*t^15 - 37*t^14 - 37*t^13 - 37*t^12 - 37*t^11 - 37*t^10 - 37*t^9 - 37*t^8 - 37*t^7 - 37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 17 2016 *)

%t coxG[{19,703,-37}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Feb 13 2018 *)

%Y Cf. A170758 (G.f.: (1+x)/(1-38*x)).

%K nonn

%O 0,2

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