cp's OEIS Frontend

A169371 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169371 #13 May 08 2018 00:32:57
%S A169371 1,22,462,9702,203742,4278582,89850222,1886854662,39623947902,
%T A169371 832102905942,17474161024782,366957381520422,7706105011928862,
%U A169371 161828205250506102,3398392310260628142,71366238515473190982
%N A169371 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169371 The initial terms coincide with those of A170741, although the two sequences are eventually different.
%C A169371 First disagreement at index 31: a(31) = 102094306360577610211441129338452806400991, A170741(31) = 102094306360577610211441129338452806401222. - _Klaus Brockhaus_, Jun 17 2011
%C A169371 Computed with Magma using commands similar to those used to compute A154638.
%H A169371 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, -210).
%F A169371 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)/(210*t^31 - 20*t^30 - 20*t^29 - 20*t^28 - 20*t^27 - 20*t^26 - 20*t^25 - 20*t^24 - 20*t^23 - 20*t^22 - 20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).
%t A169371 With[{num=Total[2t^Range[30]]+t^31+1,den=Total[-20 t^Range[30]]+ 210t^31+ 1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Sep 21 2011 *)
%Y A169371 Cf. A170741 (G.f.: (1+x)/(1-21*x)).
%K A169371 nonn
%O A169371 0,2
%A A169371 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009