cp's OEIS Frontend

A170221 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.

%I A170221 #8 Dec 19 2022 15:26:28
%S A170221 1,20,380,7220,137180,2606420,49521980,940917620,17877434780,
%T A170221 339671260820,6453753955580,122621325156020,2329805177964380,
%U A170221 44266298381323220,841059669245141180,15980133715657682420
%N A170221 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
%C A170221 The initial terms coincide with those of A170739, although the two sequences are eventually different.
%C A170221 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170221 <a href="/index/Rec#order_40">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, -171).
%F A170221 G.f. (t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 +
%F A170221 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 A170221 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 A170221 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 A170221 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170221 1)/(171*t^40 - 18*t^39 - 18*t^38 - 18*t^37 - 18*t^36 - 18*t^35 - 18*t^34
%F A170221 - 18*t^33 - 18*t^32 - 18*t^31 - 18*t^30 - 18*t^29 - 18*t^28 - 18*t^27 -
%F A170221 18*t^26 - 18*t^25 - 18*t^24 - 18*t^23 - 18*t^22 - 18*t^21 - 18*t^20 -
%F A170221 18*t^19 - 18*t^18 - 18*t^17 - 18*t^16 - 18*t^15 - 18*t^14 - 18*t^13 -
%F A170221 18*t^12 - 18*t^11 - 18*t^10 - 18*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5
%F A170221 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1)
%t A170221 coxG[{40,171,-18}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 19 2022 *)
%K A170221 nonn
%O A170221 0,2
%A A170221 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009