cp's OEIS Frontend

A170208 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.

%I A170208 #8 Nov 22 2016 15:13:07
%S A170208 1,7,42,252,1512,9072,54432,326592,1959552,11757312,70543872,
%T A170208 423263232,2539579392,15237476352,91424858112,548549148672,
%U A170208 3291294892032,19747769352192,118486616113152,710919696678912,4265518180073472
%N A170208 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
%C A170208 The initial terms coincide with those of A003949, although the two sequences are eventually different.
%C A170208 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170208 <a href="/index/Rec#order_40">Index entries for linear recurrences with constant coefficients</a>, signature (5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, -15).
%F A170208 G.f. (t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 +
%F A170208 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 +
%F A170208 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 +
%F A170208 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 +
%F A170208 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170208 1)/(15*t^40 - 5*t^39 - 5*t^38 - 5*t^37 - 5*t^36 - 5*t^35 - 5*t^34 -
%F A170208 5*t^33 - 5*t^32 - 5*t^31 - 5*t^30 - 5*t^29 - 5*t^28 - 5*t^27 - 5*t^26 -
%F A170208 5*t^25 - 5*t^24 - 5*t^23 - 5*t^22 - 5*t^21 - 5*t^20 - 5*t^19 - 5*t^18 -
%F A170208 5*t^17 - 5*t^16 - 5*t^15 - 5*t^14 - 5*t^13 - 5*t^12 - 5*t^11 - 5*t^10 -
%F A170208 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1)
%t A170208 With[{num=Total[2t^Range[39]]+t^40+1,den=Total[-5 t^Range[39]]+15t^40+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Apr 19 2013 *)
%K A170208 nonn
%O A170208 0,2
%A A170208 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009