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A168816 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%I A168816 #18 Sep 17 2024 19:07:29
%S A168816 1,43,1806,75852,3185784,133802928,5619722976,236028364992,
%T A168816 9913191329664,416354035845888,17486869505527296,734448519232146432,
%U A168816 30846837807750150144,1295567187925506306048,54413821892871264854016
%N A168816 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
%C A168816 The initial terms coincide with those of A170762, although the two sequences are eventually different.
%C A168816 First disagreement at index 19: a(19) = 7111409421007917621169651186809, A170762(19) = 7111409421007917621169651187712. - _Klaus Brockhaus_, Apr 01 2011
%C A168816 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168816 G. C. Greubel, <a href="/A168816/b168816.txt">Table of n, a(n) for n = 0..500</a>
%H A168816 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, -861).
%F A168816 G.f.: (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)/(861*t^19 - 41*t^18 - 41*t^17 - 41*t^16 - 41*t^15 - 41*t^14 - 41*t^13 - 41*t^12 - 41*t^11 - 41*t^10 - 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).
%t A168816 CoefficientList[Series[(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)/(861*t^19 -41*t^18 -41*t^17 -41*t^16 -41*t^15 -41*t^14 - 41*t^13 -41*t^12 -41*t^11 -41*t^10 -41*t^9 -41*t^8 -41*t^7 -41*t^6 -41*t^5 - 41*t^4 -41*t^3 -41*t^2 -41*t +1), {t,0,50}], t] (* _G. C. Greubel_, Nov 21 2016 *)
%t A168816 coxG[{19,861,-41}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 17 2024 *)
%Y A168816 Cf. A170762 (G.f.: (1+x)/(1-42*x)).
%K A168816 nonn,easy
%O A168816 0,2
%A A168816 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009