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A169296 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.

%I A169296 #12 May 10 2018 01:42:10
%S A169296 1,43,1806,75852,3185784,133802928,5619722976,236028364992,
%T A169296 9913191329664,416354035845888,17486869505527296,734448519232146432,
%U A169296 30846837807750150144,1295567187925506306048,54413821892871264854016
%N A169296 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
%C A169296 The initial terms coincide with those of A170762, although the two sequences are eventually different.
%C A169296 First disagreement at index 29: a(29) = 121464281835181416458609936792235618335811697785, A170762(29) = 121464281835181416458609936792235618335811698688. - _Klaus Brockhaus_, Jun 03 2011
%C A169296 Computed with Magma using commands similar to those used to compute A154638.
%H A169296 <a href="/index/Rec#order_29">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, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, -861).
%F A169296 G.f.: (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)/(861*t^29 - 41*t^28 - 41*t^27 - 41*t^26 - 41*t^25 - 41*t^24 - 41*t^23 - 41*t^22 - 41*t^21 - 41*t^20 - 41*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 A169296 coxG[{29,861,-41}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Mar 22 2017 *)
%Y A169296 Cf. A170762 (G.f.: (1+x)/(1-42*x)).
%K A169296 nonn
%O A169296 0,2
%A A169296 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009