cp's OEIS Frontend

A170175 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.

%I A170175 #8 Nov 22 2016 15:51:40
%S A170175 1,22,462,9702,203742,4278582,89850222,1886854662,39623947902,
%T A170175 832102905942,17474161024782,366957381520422,7706105011928862,
%U A170175 161828205250506102,3398392310260628142,71366238515473190982
%N A170175 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
%C A170175 The initial terms coincide with those of A170741, although the two sequences are eventually different.
%C A170175 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170175 <a href="/index/Rec#order_39">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, 20, 20, 20, 20, 20, 20, 20, 20, -210).
%F A170175 G.f. (t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 +
%F A170175 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 +
%F A170175 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 +
%F A170175 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 +
%F A170175 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(210*t^39 -
%F A170175 20*t^38 - 20*t^37 - 20*t^36 - 20*t^35 - 20*t^34 - 20*t^33 - 20*t^32 -
%F A170175 20*t^31 - 20*t^30 - 20*t^29 - 20*t^28 - 20*t^27 - 20*t^26 - 20*t^25 -
%F A170175 20*t^24 - 20*t^23 - 20*t^22 - 20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 -
%F A170175 20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 -
%F A170175 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 -
%F A170175 20*t^2 - 20*t + 1)
%t A170175 With[{num=Total[2t^Range[38]]+t^39+1,den=Total[-20 t^Range[38]]+210t^39+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Nov 25 2013 *)
%K A170175 nonn
%O A170175 0,2
%A A170175 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009