%I A072266
%S A072266 1,1,3,10,35,126,462,1717,6451,24463,93518,360031,1394582,5430530,
%T A072266 21242341,83411715,328589491,1297937234,5138431851,20380608990,
%U A072266 80960325670,322016144629,1282138331587,5109310929719,20374764059254
%N A072266 Number of words of length 2n generated by the two letters s and t that 
               reduce to the identity 1 using the relations sssssss=1, tt=1 and 
               stst=1. The generators s and t along with the three relations generate 
               the 14-element dihedral group D7.
%D A072266 H.S.M. Coxeter and W.O.J. Moser, Generators and Relations for Discrete 
               Groups, Fourth Edition, (p.134).
%F A072266 G.f.: (1-8*x+20*x^2-16*x^3+2*x^4)/(1-9*x+26*x^2-25*x^3+4*x^4). - Michael 
               Somos, Jul 21, 2002
%e A072266 The words tttt=tsts=stst=1 so a(2)=3.
%o A072266 (PARI) a(n)=if(n<1,n==0,sum(k=-(n-1)\7,(n-1)\7,C(2*n-1,n+7*k)))
%Y A072266 Sequence in context: A001700 A088218 A110556 this_sequence A085282 A149036 
               A047127
%Y A072266 Adjacent sequences: A072263 A072264 A072265 this_sequence A072267 A072268 
               A072269
%K A072266 nonn
%O A072266 0,3
%A A072266 Jamaine Paddyfoot and John Layman (jay_paddyfoot(AT)hotmail.com/layman(AT)math.vt.edu), 
               Jul 08 2002