cp's OEIS Frontend

A170605 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.

%I A170605 #8 Nov 21 2016 12:08:57
%S A170605 1,20,380,7220,137180,2606420,49521980,940917620,17877434780,
%T A170605 339671260820,6453753955580,122621325156020,2329805177964380,
%U A170605 44266298381323220,841059669245141180,15980133715657682420
%N A170605 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
%C A170605 The initial terms coincide with those of A170739, although the two sequences are eventually different.
%C A170605 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170605 <a href="/index/Rec#order_48">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, -171).
%F A170605 G.f. (t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 +
%F A170605 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 +
%F A170605 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 +
%F A170605 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 +
%F A170605 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 +
%F A170605 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170605 1)/(171*t^48 - 18*t^47 - 18*t^46 - 18*t^45 - 18*t^44 - 18*t^43 - 18*t^42
%F A170605 - 18*t^41 - 18*t^40 - 18*t^39 - 18*t^38 - 18*t^37 - 18*t^36 - 18*t^35 -
%F A170605 18*t^34 - 18*t^33 - 18*t^32 - 18*t^31 - 18*t^30 - 18*t^29 - 18*t^28 -
%F A170605 18*t^27 - 18*t^26 - 18*t^25 - 18*t^24 - 18*t^23 - 18*t^22 - 18*t^21 -
%F A170605 18*t^20 - 18*t^19 - 18*t^18 - 18*t^17 - 18*t^16 - 18*t^15 - 18*t^14 -
%F A170605 18*t^13 - 18*t^12 - 18*t^11 - 18*t^10 - 18*t^9 - 18*t^8 - 18*t^7 -
%F A170605 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1)
%t A170605 With[{num=Total[2t^Range[47]]+t^48+1,den=Total[-18 t^Range[47]]+171t^48+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Nov 10 2013 *)
%K A170605 nonn
%O A170605 0,2
%A A170605 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009