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A169417 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169417 #14 Jan 16 2024 13:54:32
%S A169417 1,20,380,7220,137180,2606420,49521980,940917620,17877434780,
%T A169417 339671260820,6453753955580,122621325156020,2329805177964380,
%U A169417 44266298381323220,841059669245141180,15980133715657682420
%N A169417 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169417 The initial terms coincide with those of A170739, although the two sequences are eventually different.
%C A169417 First disagreement is at index 32, the difference is 190. - _Klaus Brockhaus_, Jun 27 2011
%C A169417 Computed with Magma using commands similar to those used to compute A154638.
%H A169417 <a href="/index/Rec#order_32">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, -171).
%F A169417 G.f.: (t^32 + 2*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^32 - 18*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).
%F A169417 G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-18*sum(k=1..31, x^k)+171*x^32).
%t A169417 coxG[{32,171,-18}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 16 2024 *)
%Y A169417 Cf. A170739 (G.f.: (1+x)/(1-19*x) ).
%K A169417 nonn
%O A169417 0,2
%A A169417 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009