In this paper we shall show applications of the Fibonacci numbers in edge-coloured trees. In particular we determine the successive extremal graphs in the class of trees with respect to the number of (A, 2B)-edge colourings. We show connections between these numbers and Fibonacci numbers as well as the telephone numbers.
In this paper, we give formulas determining the Fibonacci polynomials of order k using the so-called generalized Newton symbols, i.e., the coefficients in the expansion of (1+z +z^2 +. . .+z^{k−1})n with respect to the powers of z.
In this paper we use the Euler-Seidel method for deriving new identities for hyperharmonic and r-Stirling numbers. The exponential generating function is determined for hyperharmonic numbers, which result is a generalization of Gosper’s identity. A classification of second order recurrence sequences is also given with the help of this method.
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This is an indicatory presentation of main definitions and theorems of Fibonomial Calculus which is a special case of ψ-extented Rota's finite operator calculus [7].
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We consider alternating sums of squares of odd and even terms of the Lucas sequence and alternating sums of their products. These alternating sums have nice representations as products of appropriate Fibonacci and Lucas numbers.
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