cp's OEIS Frontend

A170509 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.

%I A170509 #8 Dec 15 2019 15:10:13
%S A170509 1,20,380,7220,137180,2606420,49521980,940917620,17877434780,
%T A170509 339671260820,6453753955580,122621325156020,2329805177964380,
%U A170509 44266298381323220,841059669245141180,15980133715657682420
%N A170509 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
%C A170509 The initial terms coincide with those of A170739, although the two sequences are eventually different.
%C A170509 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170509 <a href="/index/Rec#order_46">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, -171).
%F A170509 G.f. (t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 +
%F A170509 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 +
%F A170509 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 +
%F A170509 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 +
%F A170509 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 +
%F A170509 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(171*t^46 - 18*t^45 -
%F A170509 18*t^44 - 18*t^43 - 18*t^42 - 18*t^41 - 18*t^40 - 18*t^39 - 18*t^38 -
%F A170509 18*t^37 - 18*t^36 - 18*t^35 - 18*t^34 - 18*t^33 - 18*t^32 - 18*t^31 -
%F A170509 18*t^30 - 18*t^29 - 18*t^28 - 18*t^27 - 18*t^26 - 18*t^25 - 18*t^24 -
%F A170509 18*t^23 - 18*t^22 - 18*t^21 - 18*t^20 - 18*t^19 - 18*t^18 - 18*t^17 -
%F A170509 18*t^16 - 18*t^15 - 18*t^14 - 18*t^13 - 18*t^12 - 18*t^11 - 18*t^10 -
%F A170509 18*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 -
%F A170509 18*t + 1)
%t A170509 coxG[{46,171,-18}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 15 2019 *)
%K A170509 nonn
%O A170509 0,2
%A A170509 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009