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In this paper, we suggest a lower and an upper bound for the GeneralizedFibonacci-p-Sequence, for different values of p. The Fibonacci-p-Sequence is ageneralization of the Classical Fibonacci Sequence. We first show that theratio of two consecutive terms in generalized Fibonacci sequence converges to ap-degree polynomial and then use this result to prove the bounds forgeneralized Fibonacci-p sequence, thereby generalizing the exponential boundsfor classical Fibonacci Sequence. Then we show how these results can be used toprove efficiency for data hiding techniques using generalized Fibonaccisequence. These steganographic techniques use generalized Fibonacci-p-Sequencefor increasing number available of bit-planes to hide data, so that more andmore data can be hidden into the higher bit-planes of any pixel without causingmuch distortion of the cover image. This bound can be used as a theoreticalproof for efficiency of those techniques, for instance it explains why more andmore data can be hidden into the higher bit-planes of a pixel, without causingconsiderable decrease in PSNR.

A Note On the Bounds for the Generalized Fibonacci-p-Sequence and its Application in Data-Hiding