cp's OEIS Frontend

A170112 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.

%I A170112 #9 May 14 2017 17:30:07
%S A170112 1,7,42,252,1512,9072,54432,326592,1959552,11757312,70543872,
%T A170112 423263232,2539579392,15237476352,91424858112,548549148672,
%U A170112 3291294892032,19747769352192,118486616113152,710919696678912,4265518180073472
%N A170112 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
%C A170112 The initial terms coincide with those of A003949, although the two sequences are eventually different.
%C A170112 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170112 <a href="/index/Rec#order_38">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, -15).
%F A170112 G.f. (t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 +
%F A170112 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 +
%F A170112 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 +
%F A170112 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 +
%F A170112 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(15*t^38 - 5*t^37 -
%F A170112 5*t^36 - 5*t^35 - 5*t^34 - 5*t^33 - 5*t^32 - 5*t^31 - 5*t^30 - 5*t^29 -
%F A170112 5*t^28 - 5*t^27 - 5*t^26 - 5*t^25 - 5*t^24 - 5*t^23 - 5*t^22 - 5*t^21 -
%F A170112 5*t^20 - 5*t^19 - 5*t^18 - 5*t^17 - 5*t^16 - 5*t^15 - 5*t^14 - 5*t^13 -
%F A170112 5*t^12 - 5*t^11 - 5*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4
%F A170112 - 5*t^3 - 5*t^2 - 5*t + 1)
%t A170112 With[{num=Total[2t^Range[37]]+t^38+1,den=Total[-5 t^Range[37]]+ 15t^38+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Nov 19 2011 *)
%K A170112 nonn
%O A170112 0,2
%A A170112 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009