A168820 - OEIS

%I #14 Dec 13 2021 16:39:29

%S 1,47,2162,99452,4574792,210440432,9680259872,445291954112,

%T 20483429889152,942237774900992,43342937645445632,1993775131690499072,

%U 91713656057762957312,4218828178657096036352,194066096218226417672192

%N Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%C The initial terms coincide with those of A170766, although the two sequences are eventually different.

%C First disagreement at index 19: a(19) = 39970430717808258425583656762311, A170766(19) = 39970430717808258425583656763392. - _Klaus Brockhaus_, Apr 01 2011

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

%H G. C. Greubel, <a href="/A168820/b168820.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 (45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, -1035).

%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)/(1035*t^19 - 45*t^18 - 45*t^17 - 45*t^16 - 45*t^15 - 45*t^14 - 45*t^13 - 45*t^12 - 45*t^11 - 45*t^10 - 45*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*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)/(1035*t^19 - 45*t^18 - 45*t^17 - 45*t^16 - 45*t^15 - 45*t^14 - 45*t^13 - 45*t^12 - 45*t^11 - 45*t^10 - 45*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Nov 21 2016 *)

%t coxG[{19,1035,-45}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 13 2021 *)

%Y Cf. A170766 (G.f.: (1+x)/(1-46*x)).

%K nonn,easy

%O 0,2

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