cp's OEIS Frontend

A170173 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.

%I A170173 #8 Jul 01 2017 16:53:27
%S A170173 1,20,380,7220,137180,2606420,49521980,940917620,17877434780,
%T A170173 339671260820,6453753955580,122621325156020,2329805177964380,
%U A170173 44266298381323220,841059669245141180,15980133715657682420
%N A170173 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
%C A170173 The initial terms coincide with those of A170739, although the two sequences are eventually different.
%C A170173 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170173 <a href="/index/Rec#order_39">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, -171).
%F A170173 G.f. (t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 +
%F A170173 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 +
%F A170173 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 +
%F A170173 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 +
%F A170173 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(171*t^39 -
%F A170173 18*t^38 - 18*t^37 - 18*t^36 - 18*t^35 - 18*t^34 - 18*t^33 - 18*t^32 -
%F A170173 18*t^31 - 18*t^30 - 18*t^29 - 18*t^28 - 18*t^27 - 18*t^26 - 18*t^25 -
%F A170173 18*t^24 - 18*t^23 - 18*t^22 - 18*t^21 - 18*t^20 - 18*t^19 - 18*t^18 -
%F A170173 18*t^17 - 18*t^16 - 18*t^15 - 18*t^14 - 18*t^13 - 18*t^12 - 18*t^11 -
%F A170173 18*t^10 - 18*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 -
%F A170173 18*t^2 - 18*t + 1)
%t A170173 coxG[{39,171,-18}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 01 2017 *)
%K A170173 nonn
%O A170173 0,2
%A A170173 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009