cp's OEIS Frontend

A170542 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.

%I A170542 #8 Nov 21 2016 12:44:33
%S A170542 1,5,20,80,320,1280,5120,20480,81920,327680,1310720,5242880,20971520,
%T A170542 83886080,335544320,1342177280,5368709120,21474836480,85899345920,
%U A170542 343597383680,1374389534720,5497558138880,21990232555520,87960930222080
%N A170542 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
%C A170542 The initial terms coincide with those of A003947, although the two sequences are eventually different.
%C A170542 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170542 <a href="/index/Rec#order_47">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, 3, 3, 3, 3, 3, 3, -6).
%F A170542 G.f. (t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 +
%F A170542 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 +
%F A170542 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 A170542 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 A170542 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 A170542 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(6*t^47 -
%F A170542 3*t^46 - 3*t^45 - 3*t^44 - 3*t^43 - 3*t^42 - 3*t^41 - 3*t^40 - 3*t^39 -
%F A170542 3*t^38 - 3*t^37 - 3*t^36 - 3*t^35 - 3*t^34 - 3*t^33 - 3*t^32 - 3*t^31 -
%F A170542 3*t^30 - 3*t^29 - 3*t^28 - 3*t^27 - 3*t^26 - 3*t^25 - 3*t^24 - 3*t^23 -
%F A170542 3*t^22 - 3*t^21 - 3*t^20 - 3*t^19 - 3*t^18 - 3*t^17 - 3*t^16 - 3*t^15 -
%F A170542 3*t^14 - 3*t^13 - 3*t^12 - 3*t^11 - 3*t^10 - 3*t^9 - 3*t^8 - 3*t^7 -
%F A170542 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1)
%t A170542 With[{num=Total[2t^Range[46]]+t^47+1,den=Total[-3 t^Range[46]]+6t^47+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, May 26 2012 *)
%K A170542 nonn
%O A170542 0,2
%A A170542 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009