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Recently, Kalman [2] derives a number of closed-form formulas for the generalized Fibonacci sequence by matrix methods. In this note, we extend the matrix representation and show that the sums of the generalized Fibonacci numbers could be derived directly using this representation. Define k sequences of the generalized order-fc Fibonacci numbers as shown:(More)
This paper presents three simple and efficient algorithms for generating, ranking and unranking t-ary trees in a lexicographic order. The simplest idea of encoding a t-ary tree with n nodes as a bit-string of length t*n is exploited to its full advantages. It is proved that the lexicographic order in the set of t-ary trees with n nodes is preserved in the(More)