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A072844
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Number of words of length 2n+1 generated by the two letters s and t that reduce to the identity 1 by 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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0
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0, 0, 0, 1, 9, 55, 286, 1365, 6188, 27132, 116281, 490337, 2043275, 8439210, 34621041, 141290436, 574274008, 2326683921, 9402807817, 37923176863, 152705590518, 614111175965, 2467123420524, 9903167265124, 39725253489545
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OFFSET
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1,5
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REFERENCES
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H.S.M. Coxeter and W.O.J. Moser, Generators and Relations for Discrete Groups, Fourth Edition, (p.134).
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LINKS
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FORMULA
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Conjecture: a(n) = 9*a(n-1) - 26*a(n-2) + 25*a(n-3) - 4*a(n-4).
Empirical g.f.: x^4 / ((1 - 4*x)*(1 - 5*x + 6*x^2 - x^3)). - Colin Barker, Feb 24 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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