cp's OEIS Frontend

A170056 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170056 #8 Apr 14 2020 15:43:39
%S A170056 1,47,2162,99452,4574792,210440432,9680259872,445291954112,
%T A170056 20483429889152,942237774900992,43342937645445632,1993775131690499072,
%U A170056 91713656057762957312,4218828178657096036352,194066096218226417672192
%N A170056 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170056 The initial terms coincide with those of A170766, although the two sequences are eventually different.
%C A170056 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170056 <a href="/index/Rec#order_36">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, 45, 45, 45, 45, 45, 45, 45, 45, 45, -1035).
%F A170056 G.f. (t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170056 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170056 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170056 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
%F A170056 + 2*t^3 + 2*t^2 + 2*t + 1)/(1035*t^36 - 45*t^35 - 45*t^34 - 45*t^33 -
%F A170056 45*t^32 - 45*t^31 - 45*t^30 - 45*t^29 - 45*t^28 - 45*t^27 - 45*t^26 -
%F A170056 45*t^25 - 45*t^24 - 45*t^23 - 45*t^22 - 45*t^21 - 45*t^20 - 45*t^19 -
%F A170056 45*t^18 - 45*t^17 - 45*t^16 - 45*t^15 - 45*t^14 - 45*t^13 - 45*t^12 -
%F A170056 45*t^11 - 45*t^10 - 45*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4
%F A170056 - 45*t^3 - 45*t^2 - 45*t + 1)
%t A170056 coxG[{36,1035,-45}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 14 2020 *)
%K A170056 nonn
%O A170056 0,2
%A A170056 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009