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A169294 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.

%I A169294 #12 May 10 2018 01:41:25
%S A169294 1,41,1640,65600,2624000,104960000,4198400000,167936000000,
%T A169294 6717440000000,268697600000000,10747904000000000,429916160000000000,
%U A169294 17196646400000000000,687865856000000000000,27514634240000000000000
%N A169294 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
%C A169294 The initial terms coincide with those of A170760, although the two sequences are eventually different.
%C A169294 First disagreement at index 29: a(29) = 29543613555550453759999999999999999999999999180, A170760(29) = 29543613555550453760000000000000000000000000000. - _Klaus Brockhaus_, Jun 03 2011
%C A169294 Computed with Magma using commands similar to those used to compute A154638.
%H A169294 <a href="/index/Rec#order_29">Index entries for linear recurrences with constant coefficients</a>, signature (39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, -780).
%F A169294 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)/(780*t^29 - 39*t^28 - 39*t^27 - 39*t^26 - 39*t^25 - 39*t^24 - 39*t^23 - 39*t^22 - 39*t^21 - 39*t^20 - 39*t^19 - 39*t^18 - 39*t^17 - 39*t^16 - 39*t^15 - 39*t^14 - 39*t^13 - 39*t^12 - 39*t^11 - 39*t^10 - 39*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5 - 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1).
%t A169294 coxG[{29,780,-39}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 15 2015 *)
%Y A169294 Cf. A170760 (G.f.: (1+x)/(1-40*x)).
%K A169294 nonn
%O A169294 0,2
%A A169294 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009