Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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(±1)-INVARIANT SEQUENCES AND TRUNCATED FIBONACCI SEQUENCES OF THE SECOND KIND

  • CHOI GYOUNG-SIK (Department of Mathematics Education Kyungpook University) ;
  • HWANG SUK-GEUN (Department of Mathematics Education Kyungpook University) ;
  • KIM IK-PYO (Department of Mathematics Education Kyungpook University)
  • Published : 2005.07.01
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Abstract

In this paper we present another characterization of (${\pm}1$)-invariant sequences. We also introduce truncated Fibonacci and Lucas sequences of the second kind and show that a sequence $x\;{\in}\;R^{\infty}$ is (-1)-invariant(l-invariant resp.) if and only if $D[_x^0]$ is perpendicular to every truncated Fibonacci(truncated Lucas resp.) sequence of the second kind where $$D=diag((-1)^0,\; (-1)^1,\;(-1)^2,{\ldots})$$.

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References

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