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A169369 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169369 #12 May 08 2018 00:31:30
%S A169369 1,20,380,7220,137180,2606420,49521980,940917620,17877434780,
%T A169369 339671260820,6453753955580,122621325156020,2329805177964380,
%U A169369 44266298381323220,841059669245141180,15980133715657682420
%N A169369 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169369 The initial terms coincide with those of A170739, although the two sequences are eventually different.
%C A169369 First disagreement at index 31: a(31) = 4609332357943904300910190388118665867830, A170739(31) = 4609332357943904300910190388118665868020. - _Klaus Brockhaus_, Jun 17 2011
%C A169369 Computed with Magma using commands similar to those used to compute A154638.
%H A169369 <a href="/index/Rec#order_31">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, -171).
%F A169369 G.f.: (t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 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 + 2*t^3 + 2*t^2 + 2*t + 1)/(171*t^31 - 18*t^30 - 18*t^29 - 18*t^28 - 18*t^27 - 18*t^26 - 18*t^25 - 18*t^24 - 18*t^23 - 18*t^22 - 18*t^21 - 18*t^20 - 18*t^19 - 18*t^18 - 18*t^17 - 18*t^16 - 18*t^15 - 18*t^14 - 18*t^13 - 18*t^12 - 18*t^11 - 18*t^10 - 18*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1).
%t A169369 coxG[{31,171,-18}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Nov 03 2015 *)
%Y A169369 Cf. A170739 (G.f.: (1+x)/(1-19*x)).
%K A169369 nonn
%O A169369 0,2
%A A169369 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009