cp's OEIS Frontend

A170254 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.

%I A170254 #9 Nov 22 2016 11:38:49
%S A170254 1,5,20,80,320,1280,5120,20480,81920,327680,1310720,5242880,20971520,
%T A170254 83886080,335544320,1342177280,5368709120,21474836480,85899345920,
%U A170254 343597383680,1374389534720,5497558138880,21990232555520,87960930222080
%N A170254 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
%C A170254 The initial terms coincide with those of A003947, although the two sequences are eventually different.
%C A170254 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170254 <a href="/index/Rec#order_41">Index entries for linear recurrences with constant coefficients</a>, signature (3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -6).
%F A170254 G.f. (t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170254 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A170254 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +
%F A170254 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +
%F A170254 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 +
%F A170254 1)/(6*t^41 - 3*t^40 - 3*t^39 - 3*t^38 - 3*t^37 - 3*t^36 - 3*t^35 -
%F A170254 3*t^34 - 3*t^33 - 3*t^32 - 3*t^31 - 3*t^30 - 3*t^29 - 3*t^28 - 3*t^27 -
%F A170254 3*t^26 - 3*t^25 - 3*t^24 - 3*t^23 - 3*t^22 - 3*t^21 - 3*t^20 - 3*t^19 -
%F A170254 3*t^18 - 3*t^17 - 3*t^16 - 3*t^15 - 3*t^14 - 3*t^13 - 3*t^12 - 3*t^11 -
%F A170254 3*t^10 - 3*t^9 - 3*t^8 - 3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 -
%F A170254 3*t + 1)
%t A170254 With[{num=Total[2t^Range[40]]+t^41+1,den=Total[-3 t^Range[40]]+6t^41+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Nov 10 2011 *)
%K A170254 nonn
%O A170254 0,2
%A A170254 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009