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A072266
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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.
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1
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1, 1, 3, 10, 35, 126, 462, 1717, 6451, 24463, 93518, 360031, 1394582, 5430530, 21242341, 83411715, 328589491, 1297937234, 5138431851, 20380608990, 80960325670, 322016144629, 1282138331587, 5109310929719, 20374764059254
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| H.S.M. Coxeter and W.O.J. Moser, Generators and Relations for Discrete Groups, Fourth Edition, (p.134).
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FORMULA
| 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
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EXAMPLE
| The words tttt=tsts=stst=1 so a(2)=3.
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PROG
| (PARI) a(n)=if(n<1, n==0, sum(k=-(n-1)\7, (n-1)\7, C(2*n-1, n+7*k)))
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CROSSREFS
| Sequence in context: A001700 A088218 A110556 * A085282 A149036 A047127
Adjacent sequences: A072263 A072264 A072265 * A072267 A072268 A072269
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KEYWORD
| nonn
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AUTHOR
| Jamaine Paddyfoot and John Layman (jay_paddyfoot(AT)hotmail.com/layman(AT)math.vt.edu), Jul 08 2002
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