cp's OEIS Frontend

A169020 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.

%I A169020 #15 Nov 25 2016 10:56:38
%S A169020 1,7,42,252,1512,9072,54432,326592,1959552,11757312,70543872,
%T A169020 423263232,2539579392,15237476352,91424858112,548549148672,
%U A169020 3291294892032,19747769352192,118486616113152,710919696678912,4265518180073472
%N A169020 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
%C A169020 The initial terms coincide with those of A003949, although the two sequences are eventually different.
%C A169020 First disagreement at index 24: a(24) = 5528111561375219691, A003949(24) = 5528111561375219712. - _Klaus Brockhaus_, Apr 20 2011
%C A169020 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169020 Vincenzo Librandi, <a href="/A169020/b169020.txt">Table of n, a(n) for n = 0..200</a>
%H A169020 <a href="/index/Rec#order_24">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, -15).
%F A169020 G.f.: (t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 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 + 1)/(15*t^24 - 5*t^23 - 5*t^22 - 5*t^21 - 5*t^20 - 5*t^19 - 5*t^18 - 5*t^17 - 5*t^16 - 5*t^15 - 5*t^14 - 5*t^13 - 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 - 5*t^3 - 5*t^2 - 5*t + 1).
%t A169020 With[{num=Total[2t^Range[23]]+t^24+1,den=Total[-5 t^Range[23]]+15t^24+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Jun 29 2014 *)
%Y A169020 Cf. A003949 (G.f.: (1+x)/(1-6*x)).
%K A169020 nonn
%O A169020 0,2
%A A169020 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009