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A169440 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169440 #18 May 08 2018 00:25:50
%S A169440 1,43,1806,75852,3185784,133802928,5619722976,236028364992,
%T A169440 9913191329664,416354035845888,17486869505527296,734448519232146432,
%U A169440 30846837807750150144,1295567187925506306048,54413821892871264854016
%N A169440 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169440 The initial terms coincide with those of A170762, although the two sequences are eventually different.
%C A169440 First disagreement is at index 32, the difference is 903. - _Klaus Brockhaus_, Jun 30 2011
%C A169440 Computed with Magma using commands similar to those used to compute A154638.
%H A169440 <a href="/index/Rec#order_32">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, 41, 41, 41, -861).
%F A169440 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)/(861*t^32 - 41*t^31 - 41*t^30 - 41*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).
%F A169440 G.f.: (1+2*sum(k=1..31,x^k)+x^32)/(1-41*sum(k=1..31,x^k)+861*x^32).
%t A169440 coxG[{32,861,-41}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 22 2016 *)
%Y A169440 Cf. A170762 (G.f.: (1+x)/(1-42*x) ).
%K A169440 nonn
%O A169440 0,2
%A A169440 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009