cp's OEIS Frontend

A170557 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.

%I A170557 #8 Mar 20 2023 08:38:33
%S A170557 1,20,380,7220,137180,2606420,49521980,940917620,17877434780,
%T A170557 339671260820,6453753955580,122621325156020,2329805177964380,
%U A170557 44266298381323220,841059669245141180,15980133715657682420
%N A170557 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
%C A170557 The initial terms coincide with those of A170739, although the two sequences are eventually different.
%C A170557 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170557 <a href="/index/Rec#order_47">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, -171).
%F A170557 G.f. (t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 +
%F A170557 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 +
%F A170557 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 A170557 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 A170557 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 A170557 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(171*t^47 -
%F A170557 18*t^46 - 18*t^45 - 18*t^44 - 18*t^43 - 18*t^42 - 18*t^41 - 18*t^40 -
%F A170557 18*t^39 - 18*t^38 - 18*t^37 - 18*t^36 - 18*t^35 - 18*t^34 - 18*t^33 -
%F A170557 18*t^32 - 18*t^31 - 18*t^30 - 18*t^29 - 18*t^28 - 18*t^27 - 18*t^26 -
%F A170557 18*t^25 - 18*t^24 - 18*t^23 - 18*t^22 - 18*t^21 - 18*t^20 - 18*t^19 -
%F A170557 18*t^18 - 18*t^17 - 18*t^16 - 18*t^15 - 18*t^14 - 18*t^13 - 18*t^12 -
%F A170557 18*t^11 - 18*t^10 - 18*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5 - 18*t^4
%F A170557 - 18*t^3 - 18*t^2 - 18*t + 1)
%t A170557 coxG[{47,171,-18}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Mar 20 2023 *)
%K A170557 nonn
%O A170557 0,2
%A A170557 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009