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(±1)-INVARIANT SEQUENCES AND TRUNCATED FIBONACCI SEQUENCES OF THE SECOND KIND
In this paper we present another characterization of (<TEX>${\pm}1$</TEX>)-invariant sequences. We also introduce truncated Fibonacci and Lucas sequences of the second kind and show that a sequence <TEX>$x\;{\in}\;R^{\infty}$</TEX> is (-1)-invariant(l-invariant resp.) if and only if <TEX>$D[_x^0]$</TEX> is perpendicular to every truncated Fibonacci(truncated Lucas resp.) sequence of the second kind where …