cp's OEIS Frontend

A168810 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%I A168810 #12 Nov 24 2016 16:24:35
%S A168810 1,37,1332,47952,1726272,62145792,2237248512,80540946432,
%T A168810 2899474071552,104381066575872,3757718396731392,135277862282330112,
%U A168810 4870003042163884032,175320109517899825152,6311523942644393705472
%N A168810 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
%C A168810 The initial terms coincide with those of A170756, although the two sequences are eventually different.
%C A168810 First disagreement at index 19: a(19) = 381633717544149815208362114406, A170756(19) = 381633717544149815208362115072. - _Klaus Brockhaus_, Apr 01 2011
%C A168810 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168810 G. C. Greubel, <a href="/A168810/b168810.txt">Table of n, a(n) for n = 0..500</a>
%H A168810 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, -630).
%F A168810 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)/(630*t^19 - 35*t^18 - 35*t^17 - 35*t^16 - 35*t^15 - 35*t^14 - 35*t^13 - 35*t^12 - 35*t^11 - 35*t^10 - 35*t^9 - 35*t^8 - 35*t^7 - 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 - 35*t^2 - 35*t + 1).
%t A168810 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)/(630*t^19 - 35*t^18 - 35*t^17 - 35*t^16 - 35*t^15 - 35*t^14 - 35*t^13 - 35*t^12 - 35*t^11 - 35*t^10 - 35*t^9 - 35*t^8 - 35*t^7 - 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 - 35*t^2 - 35*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 17 2016 *)
%Y A168810 Cf. A170756 (G.f.: (1+x)/(1-36*x)).
%K A168810 nonn
%O A168810 0,2
%A A168810 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009