cp's OEIS Frontend

A170077 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.

%I A170077 #6 Nov 26 2016 10:03:06
%S A170077 1,20,380,7220,137180,2606420,49521980,940917620,17877434780,
%T A170077 339671260820,6453753955580,122621325156020,2329805177964380,
%U A170077 44266298381323220,841059669245141180,15980133715657682420
%N A170077 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
%C A170077 The initial terms coincide with those of A170739, although the two sequences are eventually different.
%C A170077 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170077 <a href="/index/Rec#order_37">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, -171).
%F A170077 G.f. (t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 +
%F A170077 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 +
%F A170077 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 +
%F A170077 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 +
%F A170077 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(171*t^37 - 18*t^36 - 18*t^35 -
%F A170077 18*t^34 - 18*t^33 - 18*t^32 - 18*t^31 - 18*t^30 - 18*t^29 - 18*t^28 -
%F A170077 18*t^27 - 18*t^26 - 18*t^25 - 18*t^24 - 18*t^23 - 18*t^22 - 18*t^21 -
%F A170077 18*t^20 - 18*t^19 - 18*t^18 - 18*t^17 - 18*t^16 - 18*t^15 - 18*t^14 -
%F A170077 18*t^13 - 18*t^12 - 18*t^11 - 18*t^10 - 18*t^9 - 18*t^8 - 18*t^7 -
%F A170077 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1)
%K A170077 nonn
%O A170077 0,2
%A A170077 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009