A169204 - OEIS

%I #12 Sep 30 2019 14:19:19

%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)^27 = I.

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

%C First disagreement at index 27: a(27) = 801311695774083274277408250529829634978085831, A170766(27) = 801311695774083274277408250529829634978086912. - _Klaus Brockhaus_, May 07 2011

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

%H <a href="/index/Rec#order_27">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, 45, 45, 45, 45, 45, 45, 45, 45, -1035).

%F G.f.: (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)/(1035*t^27 - 45*t^26 - 45*t^25 - 45*t^24 - 45*t^23 - 45*t^22 - 45*t^21 - 45*t^20 - 45*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 coxG[{27,1035,-45}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 30 2019 *)

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

%K nonn

%O 0,2

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