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A169368 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169368 #12 May 08 2018 00:31:02
%S A169368 1,19,342,6156,110808,1994544,35901792,646232256,11632180608,
%T A169368 209379250944,3768826516992,67838877305856,1221099791505408,
%U A169368 21979796247097344,395636332447752192,7121453984059539456
%N A169368 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169368 The initial terms coincide with those of A170738, although the two sequences are eventually different.
%C A169368 First disagreement at index 31: a(31) = 864826032550163466760080580787470073685, A170738(31) = 864826032550163466760080580787470073856. - _Klaus Brockhaus_, Jun 17 2011
%C A169368 Computed with Magma using commands similar to those used to compute A154638.
%H A169368 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, -153).
%F A169368 G.f.: (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)/(153*t^31 - 17*t^30 - 17*t^29 - 17*t^28 - 17*t^27 - 17*t^26 - 17*t^25 - 17*t^24 - 17*t^23 - 17*t^22 - 17*t^21 - 17*t^20 - 17*t^19 - 17*t^18 - 17*t^17 - 17*t^16 - 17*t^15 - 17*t^14 - 17*t^13 - 17*t^12 - 17*t^11 - 17*t^10 - 17*t^9 - 17*t^8 - 17*t^7 - 17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1).
%t A169368 coxG[{31,153,-17}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 30 2016 *)
%Y A169368 Cf. A170738 (G.f.: (1+x)/(1-18*x)).
%K A169368 nonn
%O A169368 0,2
%A A169368 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009