cp's OEIS Frontend

A170413 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.

%I A170413 #8 Mar 01 2023 10:10:20
%S A170413 1,20,380,7220,137180,2606420,49521980,940917620,17877434780,
%T A170413 339671260820,6453753955580,122621325156020,2329805177964380,
%U A170413 44266298381323220,841059669245141180,15980133715657682420
%N A170413 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
%C A170413 The initial terms coincide with those of A170739, although the two sequences are eventually different.
%C A170413 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170413 <a href="/index/Rec#order_44">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, -171).
%F A170413 G.f. (t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 +
%F A170413 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170413 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170413 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170413 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4
%F A170413 + 2*t^3 + 2*t^2 + 2*t + 1)/(171*t^44 - 18*t^43 - 18*t^42 - 18*t^41 -
%F A170413 18*t^40 - 18*t^39 - 18*t^38 - 18*t^37 - 18*t^36 - 18*t^35 - 18*t^34 -
%F A170413 18*t^33 - 18*t^32 - 18*t^31 - 18*t^30 - 18*t^29 - 18*t^28 - 18*t^27 -
%F A170413 18*t^26 - 18*t^25 - 18*t^24 - 18*t^23 - 18*t^22 - 18*t^21 - 18*t^20 -
%F A170413 18*t^19 - 18*t^18 - 18*t^17 - 18*t^16 - 18*t^15 - 18*t^14 - 18*t^13 -
%F A170413 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 A170413 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1)
%t A170413 coxG[{44,171,-18}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Mar 01 2023 *)
%K A170413 nonn
%O A170413 0,2
%A A170413 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009