cp's OEIS Frontend

A170366 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

%I A170366 #9 Nov 21 2016 19:22:09
%S A170366 1,21,420,8400,168000,3360000,67200000,1344000000,26880000000,
%T A170366 537600000000,10752000000000,215040000000000,4300800000000000,
%U A170366 86016000000000000,1720320000000000000,34406400000000000000
%N A170366 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
%C A170366 The initial terms coincide with those of A170740, although the two sequences are eventually different.
%C A170366 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170366 <a href="/index/Rec#order_43">Index entries for linear recurrences with constant coefficients</a>, signature (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).
%F A170366 G.f. (t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 +
%F A170366 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A170366 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 +
%F A170366 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 +
%F A170366 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
%F A170366 + 2*t^2 + 2*t + 1)/(190*t^43 - 19*t^42 - 19*t^41 - 19*t^40 - 19*t^39 -
%F A170366 19*t^38 - 19*t^37 - 19*t^36 - 19*t^35 - 19*t^34 - 19*t^33 - 19*t^32 -
%F A170366 19*t^31 - 19*t^30 - 19*t^29 - 19*t^28 - 19*t^27 - 19*t^26 - 19*t^25 -
%F A170366 19*t^24 - 19*t^23 - 19*t^22 - 19*t^21 - 19*t^20 - 19*t^19 - 19*t^18 -
%F A170366 19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 -
%F A170366 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 -
%F A170366 19*t^2 - 19*t + 1)
%t A170366 With[{num=Total[2t^Range[42]]+t^43+1,den=Total[-19 t^Range[42]]+ 190t^43+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Nov 01 2011 *)
%K A170366 nonn
%O A170366 0,2
%A A170366 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009