cp's OEIS Frontend

A170653 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

%I A170653 #15 Nov 21 2016 11:21:03
%S A170653 1,20,380,7220,137180,2606420,49521980,940917620,17877434780,
%T A170653 339671260820,6453753955580,122621325156020,2329805177964380,
%U A170653 44266298381323220,841059669245141180,15980133715657682420
%N A170653 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
%C A170653 The initial terms coincide with those of A170739, although the two sequences are eventually different.
%C A170653 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170653 <a href="/index/Rec#order_49">Index entries for linear recurrences with constant coefficients</a>, signature (18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, -171).
%F A170653 G.f. (t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 +
%F A170653 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170653 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A170653 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +
%F A170653 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +
%F A170653 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 +
%F A170653 1)/(171*t^49 - 18*t^48 - 18*t^47 - 18*t^46 - 18*t^45 - 18*t^44 - 18*t^43
%F A170653 - 18*t^42 - 18*t^41 - 18*t^40 - 18*t^39 - 18*t^38 - 18*t^37 - 18*t^36 -
%F A170653 18*t^35 - 18*t^34 - 18*t^33 - 18*t^32 - 18*t^31 - 18*t^30 - 18*t^29 -
%F A170653 18*t^28 - 18*t^27 - 18*t^26 - 18*t^25 - 18*t^24 - 18*t^23 - 18*t^22 -
%F A170653 18*t^21 - 18*t^20 - 18*t^19 - 18*t^18 - 18*t^17 - 18*t^16 - 18*t^15 -
%F A170653 18*t^14 - 18*t^13 - 18*t^12 - 18*t^11 - 18*t^10 - 18*t^9 - 18*t^8 -
%F A170653 18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1)
%F A170653 a(0)=1, a(1)=20, a(n)=19*a(n-1). - _Harvey P. Dale_, Jun 13 2011
%t A170653 With[{num=Total[2t^Range[ 0,49]]-1-t^49, den=Total[-18 t^Range[48]]+1+ 171t^49}, CoefficientList[ Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Jun 13 2011 *)
%K A170653 nonn
%O A170653 0,2
%A A170653 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009